The Orioles have, for all intents and purposes, completed deals with all of their arbitration-eligible players, agreeing to terms Saturday afternoon with the final one, right-handed reliever Darren O’Day on a two-year extension worth a guaranteed $5.8 million.

The Orioles said the deal is not yet completed, but they are nearing a multiyear extension with O’Day, who was 7-1 with a 2.28 ERA in 69 games last year.

“It is something he asked us to explore during the course of negotiations for a one-year deal and we are taking a look at it ... and there is work to be done,” Orioles executive vice president Dan Duquette said. “The club always has conditions to be met before agreeing to a multiyear deal and currently not all of those conditions have been met.”

Duquette would not go into specifics, but the Orioles, as policy, require physicals for contract extensions. The club’s pitchers are scheduled to take their annual physicals in Sarasota, Fla., on Wednesday, so it’s conceivable that an announcement will not be made until after that.

However, O’Day’s agency, the Beverly Hills Sports Council, announced on Twitter that its client had agreed to a two-year deal with a team option for 2015.

According to an industry source, O’Day will be paid $2.2 million in 2013, $3.2 million in 2014 and the club holds a $4.25 million option for 2015 that includes a $400,000 buyout.

O’Day, who made $1.35 million in 2012, was seeking $3.2 million in arbitration this winter and the Orioles had countered with $1.8 million. The 30-year-old was eligible for one more year of arbitration next winter before becoming a free agent after the 2014 season. Now, the affable sidearmer can be under team control through 2015 -- welcomed security for a player claimed off of waivers from the Texas Rangers last offseason after an injury-shortened 2011 season.

O’Day absolutely flourished in Baltimore in 2012, eventually becoming the top set-up man to closer Jim Johnson. In four of the six full months he pitched last season, O’Day posted an ERA under 2.50, including allowing just one earned run in 12 innings in August.

“If you look at Darren O’Day’s body of work and his track record over the years, he’s been among the top eight relievers in the business,” Duquette said. “He’s very dependable and he can pitch at the key points in a game when needed to get the club out of a jam or to protect a lead in late innings. He is a good pitcher.”

Agreeing to terms with O’Day also was significant in that the club will not go to an arbitration hearing with any of its players in 2013, the sixth time in seven years it has done that. This November, the Orioles had 13 potential arbitration cases.

“You look at all these deals very carefully and you try to reward the player with a fair compensation,” Duquette said.

MASNsports.com first reported that the Orioles and O’Day were nearing a deal. CBSSports.com had some contractual details first.

dan.connolly@baltsun.com