Coach Mike Singletary made the announcement on his regular KNBR radio show Tuesday morning and the team later tweeted a reference to it.
The move comes a day after Singletary said he was contemplating the switch from Troy Smith back to the 2005 No. 1 overall draft pick following a 34-16 loss at Green Bay Packers last Sunday. The 49ers (4-8) face a key game at home against NFC West rival Seattle on Sunday.
Later Tuesday, the 49ers announced that Johnnie Lynn the secondary coach and special assistant to Singletary has resigned for personal reasons.
Alex Smith dislocated his non-throwing left shoulder Oct. 24 at Carolina Panthers and hasn't played since, despite being medically cleared several weeks ago.
Singletary has said he will pick a starting QB each week.
"Our quarterback is going to be Alex Smith," Singletary told KNBR. "We felt at this time, Alex with his experience and all of the other things, he would give us the best chance to win at this particular time, at this time of the year. Still very confident in what Troy has been able to do and would not rule out at any point in time him playing again. Right now it's just a matter of looking where we are in the season and the opportunity we have before us."
Alex Smith has completed 143 of 242 passes for 1,554 yards and nine touchdowns with nine interceptions and 13 sacks this season. He has a subpar 75.0 quarterback rating. This very well could be his last hurrah and farewell season in San Francisco.
The 26-year-old Smith, who took over as the starter from the now-departed Shaun Hill at halftime on Oct. 25, 2009, at Houston, is in the final year of his contract with a team trying to end a seven-year playoff drought despite a surprising 0-5 start.
Troy Smith, the 2006 Heisman Trophy winner with Ohio State, went 3-2 in five games as the starter after signing with the 49ers in September following his release by Baltimore. His late timing joining the Niners put him behind in learning the playbook, but not so much that Singletary didn't have confidence he could do the job -- picking the third-stringer over backup David Carr to replace the injured Alex Smith against the Panthers.
Troy Smith is 66 for 126 and has passed for 1,023 yards and four touchdowns, including throwing for 356 yards in a 23-20 overtime victory over the St. Louis Rams on Nov. 14.
"I think the most important thing is the guys understand I'm going to go with the guy I figure will give us the best opportunity to win. I think they know that about me," Singletary told the radio station. "We're trying to win games and that's really the bottom line. ...
"Because of the experience, obviously [Alex] knows the playbook. He's been here, has been in the system, has gone through training camp, the whole nine yards. I just feel that right now he gives us the best chance to win."