Tinkle took the Grizzlies to the NCAA tournament three times in his tenure with the team. Montana finished below .500 only once during that span.
The 48-year-old replaces Craig Robinson, brother-in-law of President Barack Obama, after he was fired earlier this month following six seasons with the Beavers in which he failed to make the NCAA tournament. The once-proud Beavers have not been to the NCAA tournament since 1990.
Tinkle went 158-91 with the Grizzlies, compiling the second-most victories in school history. The only slight on his résumé at Montana was an inability to get an NCAA tournament victory, something the Grizzlies have not done since beating Nevada in the first round in 2006.
"I met with Coach Tinkle for several hours last week and came away very impressed with him. His success on the basketball court as a coach and player is well documented, but even more so, I was impressed with his demeanor, family and philosophy," Oregon State athletic director Bob De Carolis said in a statement Monday night.
The Beavers are expected to introduce Tinkle at a news conference Wednesday in Corvallis.
Montana has a history of producing successful coaches, including Jud Heathcote, Mike Montgomery and Larry Krystkowiak. Heathcote went from Montana to Michigan State, Montgomery went to Stanford, and Krystkowiak left Montana for the NBA before ending up at Utah and starting to turn around the Utes' program last season.
Tinkle was an assistant under Krystkowiak and often draws comparisons to him.
Robinson was unexpectedly fired May 5, a little more than a month after De Carolis announced Michelle Obama's older brother would return for a seventh season as basketball coach.
Robinson went 94-105 overall -- and 39-69 in the Pac-12 -- with Oregon State after spending two seasons as Brown's coach. The Beavers made the postseason four times under Robinson but all were appearances in the lower-tier College Basketball Invitational.
Oregon State went 16-16 this past season, including 8-10 in the Pac-12, and was bounced in the first round of the CBI by Radford.
Former UCLA coach Ben Howland and former Trail Blazer Damon Stoudamire were both rumored to be candidates for the job.
Tinkle will face a challenge with a Beavers roster decimated by graduation and transfers. Oregon State has no returning starters in 2014-15 after Eric Moreland declared early for the NBA draft, Hallice Cooke decided to transfer and Challe Barton left to play professionally overseas. Leading scorer Roberto Nelson, Devon Collier and Angus Brandt were seniors last season and won't be back, either.
Cooke announced Monday that he will play at Iowa State.
Tinkle, who played at forward for the Grizzlies during his college career, is Oregon State's 21st men's basketball coach.