HOUSTON -- - Jake Odorizzi decided to fashion his game like Zack Greinke's when he was still in high school.

Now entering his 10th season in the majors, the right-hander has become teammates with the man he's looked up to for so long after Odorizzi signed with the Houston Astros.

"I'm looking forward to getting to know him on a personal level and talking pitching with him because he's got a great mind for pitching," Odorizzi said Tuesday. "He's the guy that mechanically I tried to emulate, repertoire, everything like that. So, if I can keep doing it, as long as he's done it, I'd be pretty darn happy with myself."

Odorizzi and the Astros finalized a contract Monday that guarantees $20.25 million over two years or $23.5 million over three seasons if a player option is exercised for 2023. The deal contains additional performance bonuses that could make it worth at least $33.25 million over three years and possibly more depending on appearances in 2021 and '22.

Odorizzi enhances a Houston rotation that lost Framber Valdéz indefinitely to a broken finger this spring training. Astros ace Justin Verlander also is sidelined while recovering from Tommy John surgery.

Odorizzi adds another veteran presence to a rotation with the 37-year-old Greinke, Lance McCullers Jr., Cristian Javier and José Urquidy.

An All-Star with Minnesota in 2019, Odorizzi was limited to four starts last season because of injuries. He was 0-1 with a 6.59 ERA for the Twins during the pandemic-shortened 2020 season.

Houston general manager James Click has known Odorizzi since the pitcher played for the Tampa Bay Rays when Click worked in their front office.

"Jake was the top free agent remaining on the board in our eyes," Click said. "And certainly, the prior relationship always gives you some comfort about the player as well as the person... so it was a combination of we know how talented he is and bringing that in was something that we felt was valuable to the team."

Odorizzi, who turns 31 this month, gets a $6 million signing bonus payable in equal installments each July 15 from 2021-23, a $6 million salary this season and a $5 million salary in 2022.

The deal includes a $6.5 million player option for 2023 with a $3.25 million buyout, and the 2023 option price would escalate by $2 million each and the buyout by $1 million apiece for 20, 25 and 30 points. He would get one point for each start as a pitcher or pitching appearance of 12 or more outs during 2021 and 2022.

He said there's a chance he could be ready for Opening Day but hasn't been cleared to work out with the team yet and isn't sure whether that timetable is possible. He believes his transition to the Astros will be helped by the fact that he's played with catchers Jason Castro and Martín Maldonado in the past.

"It's very important that some guys know him enough to help him feel at home as soon as soon as possible," manager Dusty Baker said. "And this has been in the works long before Framber got injured ... so I'm just glad that we got it done. And it was in the nick of time."

Odorizzi was selected to his first All-Star team in 2019 when he made 30 starts and went a career-best 15-7 with a 3.51 ERA. He had 178 strikeouts and allowed 139 hits that season for the Twins.

He spent the last three seasons with Minnesota and has also pitched for Tampa Bay and Kansas City during his nine-year major league career. He is 62-56 with a 3.92 ERA in 195 appearances (192 starts). He's won at least 10 games four times and has four seasons with at least 30 starts.

He expects to be on the field much more this season than he was last year when he dealt with a rib injury after being hit by a line drive before being sidelined by a blister on his right middle finger.

"I want to bring some consistency, some durability, some innings," he said. "That's what I've built my career around, being consistent, taking the ball every day and giving the team a chance to win and that's what I want to do here."

The Astros placed reliever Pedro Báez on the injured list on Monday when they announced Odorizzi's signing, and Click said Tuesday that he tested positive for COVID-19. He's one of eight Houston pitchers that have been kept away from camp since last week because of COVID-19 protocols.

Bryan Abreu, Ronel Blanco and Luis Garcia were sent home on Thursday and Báez, Javier, Francis Martes, Enoli Paredes and Hector Velazquez and joined them on Friday. Click said he expects the majority of that group to be cleared to return Wednesday or Thursday.