Mack Brown and Jim Tressel struck up a conversation on the Ohio Stadium field as Texas and Ohio State warmed up before their first-ever meeting in 2005.

It was then that the two coaches realized how much they had in common.

Both programs have storied histories — the Longhorns are tied with Notre Dame for second in major-college victories, with 831, and the Buckeyes rank fifth with 808.

Both programs have enormous budgets matched only by the expectations of their die-hard fans. Both schools are located in state capitals, with strong roots in fertile recruiting territory, and neither competes with the NFL for attention.

‘‘There are so many similarities in the two schools, it really just kind of hit us that we’re living in the same place,’’ Brown recalled on Friday. ‘‘We just have different colors and different weather.’’

Since that conversation in September 2005, Brown led Texas to a national title, which gives him something else in common with Tressel.

As No. 10 Ohio State (10-2) and third-ranked Texas (11-1) prepare to meet in the Fiesta Bowl on Monday night, the coaches are the most important link between the two programs. Tressel and Brown are creating lasting legacies at places where legends left their stamps in cement.

The Buckeyes train in the Woody Hayes Athletic Center. Texas plays in Darrell K. Royal/Texas Memorial Stadium.

Before Brown and Tressel arrived, the Longhorns and Buckeyes had endured lengthy droughts since their last Associated Press national titles. Hayes led Ohio State to the 1968 national championship and Royal and the Longhorns followed suit a year later.

It took decades for both schools to duplicate those achievements — and it didn’t happen until they hired Brown and Tressel.

‘‘Maybe the reality that we both know is that you can never win enough,’’ Tressel said on Friday. ‘‘Woody and Darrell probably never lost a game. I don’t know two more similar places.’’

The Longhorns chewed through three coaches — Fred Akers, David McWilliams and John Mackovic — before finding a fitting successor to Royal.

Likewise, Earle Bruce and John Cooper followed Hayes and won in Columbus, but not enough to satisfy those who pined for Woody.

Brown and Tressel have put up some gaudy numbers — Brown is 114-26 in 10 seasons with Texas, and Tressel is 83-18 in eight years with the Buckeyes — but they take different approaches to their jobs.

Brown, a 57-year-old Tennessean who graduated from Florida State, favors homespun anecdotes and is at ease bantering with reporters.

The 56-year-old Tressel, a native Ohioan, is more guarded with the media. Tressel created a stir on Friday when he refused to make starting quarterback Terrelle Pryor available to reporters on Fiesta Bowl media day — a move that doubtless would have brought a smile from Hayes, who often battled the press.

But when it comes to football, Brown and Tressel have much in common.

Start with their compensation packages, which are among the richest in major-college football. Brown makes about $3 million per year, not including bonuses, in a contract that runs through 2016. Beginning in February, Tressel will be paid $3.5 million, a $1 million increase. His deal runs until 2013.

Both men won their national titles by dethroning a defending champion in a memorable bowl game; Texas defeated USC in the Rose Bowl after the 2005 season, snapping the Trojans’ 34-game win streak, and the Buckeyes knocked off Miami in the Fiesta Bowl after the 2002 season, ending the Hurricanes’ 34-game win streak.

But both Brown and Tressel had to overcome some early hurdles before returning their teams to national prominence.

When Brown arrived in 1998, the Longhorns were coming off a 4-7 season that included a once-unimaginable 66-3 home loss to UCLA. Texas’ season-ticket base dropped by about 1,700 fans before Brown’s first season.

Brown quickly established stability and upgraded recruiting, and he led Texas to the Rose Bowl after the 2004 season. But Orangebloods still griped about a string of five straight losses to arch rival Oklahoma — a streak Brown snapped in 2005 on his way to the national title.

‘‘They lost a few games early on, but they were rebuilding, and now coach Brown has this program back on top, back where it should be,’’ Texas quarterback Colt McCoy said.

Brown may still have his detractors, but they’ve become harder to find than tickets to a Longhorns game. Texas’ season-ticket base has gone from 38,094 to 70,000 since Brown arrived, and the school is planning a 9,000-seat expansion.

Success came faster for Tressel. But, like Brown, he also had to win over demanding followers.

Tressel had won four national titles at Youngstown State. But many fans wanted Ohio State to pursue Youngstown product Bob Stoops, who had just won the 2000 BCS national title at Oklahoma as the Buckeyes launched their search for Cooper’s replacement.

Tressel supplemented the talent Cooper left by tapping into an extensive statewide recruiting network he’d established at Youngstown State.

‘‘He has molded his players into good players,’’ said Buckeyes wide receiver Brian Hartline, who grew up in North Canton, Ohio. ‘‘He just has developed consistency throughout the program.’’

Two years into Tressel’s tenure, the Buckeyes went 14-0 and won the national title. He’s taken the Buckeyes to the BCS five times since then, including two lopsided national championship game losses, to Florida two years ago and LSU last January.

Brown came within a whisker of a shot at playing for the BCS title this year, but his Longhorns lost a Big 12 South tiebreaker to the Sooners, whom they defeated on the field. It rankles Brown, but with McCoy and a wealth of other talented players returning, Brown is primed to make another run next season.

Like the Buckeyes, the Longhorns look as if they’ll contend for national titles for years to come. Maybe Brown and Tressel will someday be seen as the standards at their respective schools, although neither expects that.

‘‘There will never be another coach Darrell Royal at Texas,’’ Brown said. ‘‘I mean, he’s the face of the program. He always will be.

‘‘One of the good things that I learned early is that I’m not chasing that legacy,’’ Brown said. ‘‘I know it’s there, and I know it’s not going to change, and I would think Jim would tell you the same thing about coach Hayes, because these are two men he and I idolized growing up.’’

Tressel shared Brown’s assessment.

‘‘We’ll never be the Woody Hayeses of the place,’’ Tressel said. ‘‘But we’re the people that have the responsibility to try to maintain that type of excellence.’’