TAMPA, Fla. -- Gio Gonzalez spent his offseason waiting for a phone call, watching hundreds of others report to big league camps while he remained unsigned in South Florida, throwing on high school and college fields in an attempt to simulate Spring Training.

Even under normal circumstances, a chance to join the Yankees would have been difficult for Gonzalez to turn down. Ultimately, his best offer -- and, Gonzalez says, the only one -- came from New York, which announced its Minor League agreement with the 33-year-old left-hander on Wednesday.

"This is a great organization, a great group of guys," Gonzalez said. "The pitching staff is incredible and the young guys they have, I think it's a no-brainer to come over here and try to participate in some action. I think these guys have a really good shot to do something wonderful and I really want to be a part of something like that."

Gonzalez earned at least $11 million in each of the last four seasons, but the two-time All-Star did not see his market develop as anticipated coming off a season in which he went 10-11 with a 4.21 ERA in 32 starts for the Nationals and Brewers, helping Milwaukee to a division title.

With right-hander Luis Severino and left-hander CC Sabathia unavailable to begin the season, Yankees general manager Brian Cashman offered Gonzalez a base salary of $3 million if he makes the big league roster, plus $300,000 for each start he makes. He can opt out on April 20.

"I'm just grateful I'm in an organization that sees something in me," Gonzalez said. "It was pretty much the only organization that saw something in me. It's something to use as fuel and try to showcase your stuff up here, and play as hard as you can. The truth is, you've still got to play."

The Hialeah, Fla., native has pitched parts of 11 seasons in the Majors with the Athletics (2008-11), Nationals (2012-18) and Brewers (2018), compiling a career record of 127-97 with a 3.69 ERA. He finished third in the 2012 National League Cy Young Award voting after leading the Majors with 21 wins.

Gonzalez said he has recently faced hitters, both at the University of Miami and at St. Thomas Aquinas High School in Fort Lauderdale, Fla.

"I think St. Thomas has some stud players that are going to wow some people in the world of baseball," Gonzalez said.

Pitching coach Larry Rothschild has been deputized to formulate a program for Gonzalez, who said he threw 88 pitches over five simulated innings on Monday and has been scheduled for a bullpen session on Thursday.

Gonzalez believes he could soon be ready to pitch in Grapefruit League games; manager Aaron Boone has suggested that Gonzalez could “piggyback” with starter Masahiro Tanaka on Saturday against the Blue Jays.

"I don't think I'm far away at all," Gonzalez said. "I've been staying with my routine, keeping up. I'm trying to keep up with baseball. I'll be ready to go. Hopefully I'll be in a game pretty soon."