SANTA CLARA — Quarterback Alex Smith will undergo surgery on his right shoulder, ending a disappointing season for the San Francisco 49ers’ former No. 1 overall draft pick.

The 49ers announced the decision late Monday night after Smith’s latest consultation with team doctors and Dr. James Andrews over the separated right shoulder that has bedeviled him for more than two months. Smith will be placed on injured reserve this week.

San Francisco also is likely to be without backup Trent Dilfer for Saturday’s home game against Cincinnati after Dilfer sustained a concussion in Sunday’s 27-7 loss to Minnesota.

Shaun Hill, a six-year veteran backup who had never attempted an NFL pass before going 22-of-27 for 181 yards and a touchdown against the Vikings, is expected to start against the Bengals.

Smith was sacked by Seattle’s Rocky Bernard on the third play of a loss to the Seahawks on Sept. 30, and he still hasn’t recovered. He sat out two games with the injury, then returned for an ugly three-game stint before the 49ers removed him from the lineup for the last four games when he complained of a still-sore shoulder and an aching forearm.

The surgery, which hasn’t yet been scheduled, and the ensuing three months of recovery will improve the weakened connection between Smith’s collarbone and shoulder. Most of his ligaments in the area were stretched and ripped during the injury.

Smith completed just 48.7 percent of his passes for 914 yards, two touchdowns and four interceptions this season, struggling along with the rest of the NFL’s lowest-ranked offense. His passer rating of 57.2 is the second-lowest among all quarterbacks who qualify for league statistics — only better than Dilfer’s 55.1.

The lingering injury also increased tensions on the 49ers (3-10) during a hugely disappointing season for a team that began the year with playoff aspirations.

San Francisco coach Mike Nolan had a lengthy public disagreement with Smith and Tom Condon, Smith’s powerful agent, over the team’s handling of Smith’s injury.

After a poor performance at Seattle last month, Smith was replaced by Dilfer, the 14th-year pro who has started six games this season. But Dilfer was taken to a hospital after a hard hit from Minnesota’s Charles Gordon just before halftime.

Dilfer was released later in the day, but Nolan declared him doubtful for Saturday.

“That kind of stuff always makes you think,” Smith said of Dilfer’s injury. “You want to be there for your teammates, but the past couple of weeks for me have been about safety and whether there’s going to be any long-term damage.”

San Francisco’s league-worst offense and passing game have been so pathetic that Hill’s effort against Minnesota produced the club’s best passer rating of the season: 106.9, or nearly twice as good as the season numbers for Smith (57.2) or Dilfer (55.1).

Hill is playing with a bandage on the dislocated index finger of his throwing hand, which swells up after practices and games. Despite the solid numbers, he led just one scoring drive and wasn’t impressed with the game tape of his first real action.

“Some things made me want to throw up, and on some things the execution was poor, but the results were good,” Hill said. “If I am the guy this week, and I’m getting the reps in practice, I look forward to that challenge.”

The 49ers also hope to sign a veteran quarterback today. Drew Olson, a practice squad member who joined the club two weeks ago, is the only other quarterback on the roster — not counting Michael Robinson, the star Penn State quarterback who’s a kick returner and a running back for San Francisco.