The happiest man in the Raiders’ facility, new millionaires aside, has to be offensive line coach Mike Tice. He must be doing cartwheels in the halls after Oakland’s free-agent haul.

“I wish I could,” he said, laughing. “I might have given it a shot.”

The Raiders re-signed left tackle Donald Penn on Wednesday, a week after they signed coveted free-agent left guard Kelechi Osemele. Oakland has one of the biggest and best offensive lines in the NFL.

“People understand that the most important person on the field is the quarterback,” Tice said, “and you have to take care of him. (General manager Reggie McKenzie) has done a great job of giving us the tools we need to do that, at a very high level.”

The Raiders finalized their agreement with Penn, a 6-foot-5, 305-pounder, late Tuesday night, sources said. That kept the free agent from making a visit to the Giants on Wednesday. Penn signed a two-year deal worth $14 million, with $7 million guaranteed, sources said.

Penn started all 16 games each of the past two seasons for Oakland, and all 16 the previous six seasons with the Bucs. Penn, 33 next month, grew up a Los Angeles Raiders fan and has long stated his desire to retire with the team.

“I’ve always wanted to play for the Raiders and I don’t care if they relocated to China,” Penn said.

Oakland also signed free-agent safety Brynden Trawick to further boost its special-teams unit. On Tuesday, the Raiders re-signed receiver and special-teams player Andre Holmes to a one-year, $1 million-plus-incentives deal, sources said.

Penn allowed two or fewer quarterback pressures in 13 of 16 games last season, according to Pro Football Focus.

He also has been one of the leaders in the locker room, and really wanted to see the team turn the corner, from 3-13 in 2014 to 7-9 last year. The scheduled Giants’ visit gave him some leverage and influenced McKenzie to increase his offer.

Penn’s return gives the Raiders one of the strongest and deepest offensive lines in the NFL, and keeps Osemele at guard. The former Baltimore offensive lineman signed a five-year, $58.5 million deal last week.

Osemele was penciled in to start at left tackle if the Raiders didn’t re-sign Penn, and Penn said he called head coach Jack Del Rio at that point to see if he was still in Oakland’s plans. Clearly, he was.

Oakland also has Rodney Hudson, last year’s big free-agent signing, at center, 2014 third-round pick Gabe Jackson at right guard and former starters Austin Howard and Menelik Watson at right tackle.

The average size of those six linemen is 6-5, 325 pounds, and the newest member also has a large nasty streak.

“Kelechi is as good of a finisher as I’ve seen, in all of my years looking at, evaluating and going against guys,” Tice said. “He is as good a finisher as there is in the league. He has great feet and tremendous lateral explosion.

“He’s special.”

Tice said Howard (knee) and Watson (Achilles) are doing “exceptionally well” in their rehabs from injuries last season. Tice is looking forward to a great competition at that spot.

Holmes, meanwhile, had 14 catches for 201 yards and four touchdowns last season, a year after he had a career-high 47 receptions for 693 yards. Holmes is also a key special-teams player.

The Raiders have starters set at every offensive position, though they would like to add another running back to push Latavius Murray. Oakland could add a safety and a middle linebacker this week, or address those needs in the draft.

Vic Tafur is a San Francisco Chronicle staff writer. Email: vtafur@sfchronicle.com Twitter: @VicTafur