Athletic director Sandy Barbour announced the hire Wednesday night. Dykes will be formally introduced at a news conference on Thursday.
Dykes, 43, led Louisiana Tech to a 9-3 season that included road wins over Illinois and Virginia and a 59-57 loss to Texas A&M. The Bulldogs were 22-15 in three seasons under Dykes.
"We think what we will do on offense will put a charge into the program and give a spike in recruiting," Dykes told ESPN on Wednesday night after meeting with his former team. "We want excitement. I want to sell it to the alumni, boosters, players, families, fans and high school coaches. I want to hit the ground running."
Dykes said the combination of California's academic reputation and financial investment to facilities and athletics made it impossible to pass up.
"The Rose Bowl is the standard every team in the league should aim for," Dykes said. "We were a two-overtime game away from playing for it when I was (an assistant) at Arizona."
Dykes said his staff has recruiting connections in California and they will "hustle" and "focus" on in-state recruiting by "selling the value of the Cal education."
"Sonny Dykes is one of the brightest offensive minds in the country, running a high-octane style of football, one that I'm certain will allow our student-athletes to thrive and that our community will love on game day," Barbour said in a statement. "However, it was far more than his history of a top-ranked offense and his proven success on the football field that solidified my decision; it was the way he described his responsibility to the University at large and his commitment to creating a climate of comprehensive excellence and success for his student-athletes."
Cal (3-9) went 2-7 in the Pac-12 under Tedford this season.
Dykes will benefit from a facilities upgrade that Tedford helped engineer. Cal opened its remodeled $321 million stadium this past season that is adjacent to a $150 million on-campus High Performance Center.
"I have great respect for the remarkable job (Tedford) did in building this and doing it the right way," Dykes said.
There was no immediate word on the terms of Dykes' contract. Cal still owes Tedford $6.9 million over the final three years of his deal, though Barbour had said the sides were working on a settlement.
Dykes' teams averaged 35.9 points and 452.5 yards per game in his tenure at Louisiana Tech. He takes over a Cal team that missed a bowl for the second time in three years. Dykes inherits a roster with some talent, most notably heralded quarterback recruit Zach Kline, who did not play as a freshman but who is in line to win the starting job next season.
Tedford, once known as a quarterback guru for his work with Joey Harrington, Kyle Boller and Aaron Rodgers, struggled in his later years at Cal to find an elite passer. The Bears had a 34-37 record in Tedford's final 5½ years, leading to his dismissal.
Dykes, the son of former Texas Tech coach Spike Dykes, is known as an offensive mastermind who runs a spread system that he honed as coordinator under Mike Leach at Texas Tech. Dykes later spent three seasons as offensive coordinator at Arizona under Mike Stoops before becoming head coach at Louisiana Tech prior to the 2010 season.
Dykes coached one of the nation's most prolific offenses at Louisiana Tech this year with the Bulldogs leading the nation with 51.5 points per contest and ranking second with 577.9 yards per game.
They started the season 9-1, losing only to Texas A&M, and were in position possibly to make it into a BCS bowl. But Louisiana Tech lost the final two games of the regular season to Utah State and San Jose State, respectively.
Louisiana Tech was offered a spot in the Advocare V100 Independence Bowl last Saturday but wanted to wait before accepting in case it got a better bid. The Independence Bowl invited Ohio instead, and the Bulldogs were left out of the bowl picture when Northern Illinois got into the Discover Orange Bowl, knocking Oklahoma out of the BCS.
Oklahoma State (7-5) then filled the Big 12's final spot in the Heart of Dallas Bowl against Purdue, while Iowa State (6-6) landed in the AutoZone Liberty Bowl to play C-USA champion Tulsa as an at-large pick and the Bulldogs were left out.
Dykes said it was very difficult to say goodbye to his Louisiana Tech players.
"You hate it for the kids," Dykes said. "We need to discuss further how the at-large bowl selections take place. We have to sort it out better because I felt we were misled a little bit by some bowls and then left without a place to play."
Now Dykes' mission is to guide Cal to better bowls and challenge programs like Oregon, Stanford, USC and UCLA.
"What we do fits well in the new Pac-12," Dykes said. "We will be fun and we will run and we will be fast. We will have our guys believing they can be better collectively than individually. and we will all buy into the team concept."
Information from ESPN's Joe Schad and The Associated Press was used in this report.