Oklahoma State athletic director Terry Don Phillips confirmed Koetter's decision in a news release issued Friday night.
"Coach Koetter informed me at approximately 7 p.m. (CST) tonight that he had been tendered an offer from Arizona State University and had accepted," Phillips said.
Arizona State officials had no comment Friday night.
However, a source close to the situation who spoke on the condition of anonymity said Koetter had agreed to a five-year contract that would pay him $700,000 per year, and that the new coach would be introduced at a news conference on the Tempe campus Saturday.
Koetter, 41, replaces Bruce Snyder, who was fired after nine seasons. Snyder will coach Arizona State in a bowl game, most likely the Las Vegas Bowl.
The Daily Oklahoman and several TV and radio stations in Oklahoma had reported Thursday and Friday that Koetter had accepted the Oklahoma State job.
But Phillips never confirmed those reports, and Koetter would not comment on any job possibilities at Boise State's practice Friday. Koetter said earlier in the week he had interviewed with Phillips and with Arizona State athletic director Gene Smith.
Koetter is considered one of the country's top young coaching prospects. Using an innovative, wide-open offense, he guided Boise State to a 25-10 record in three seasons. His first team went 6-5, followed by last year's 10-3 record, which included a 34-31 victory over Louisville in the Humanitarian Bowl.
This year's team is 9-2, with its only losses 38-31 at Arkansas and 42-25 at Washington State.
Koetter may not have been Arizona State's top choice.
Phoenix radio station KMVP reported Friday that Smith had quietly been working on a deal with TCU coach Dennis Franchione that would have matched the one offered by Alabama. But Franchione apparently couldn't resist the lure of one of college football's most storied programs.
While most of the recent speculation centered on Koetter, there was pressure from some Arizona State boosters to hire Danny White, the former Arizona State and Dallas Cowboys quarterback who coaches the Arizona Rattlers of the Arena Football League.
Snyder was fired after his teams went 6-6 last year and 6-5 this season.
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