Alcantara's deal, first reported by The Miami Herald, will be worth $56 million over five seasons.
Garcia's contract is for four years and $53 million, a source told ESPN's Jeff Passan on Sunday.
The 26-year-old Alcantara has gone 20-34 with a 3.48 ERA in four seasons with the Marlins. He started 33 games this past season for Miami, going 9-15 with a 3.19 ERA, and had 201 strikeouts in 205⅔ innings. The only other pitchers with at least 200 innings and 200 strikeouts in 2021 were Zack Wheeler and Walker Buehler.
"I think the thing that it says is it talks about the consistency," Marlins manager Don Mattingly said last month of Alcantara's 2021 numbers. "He's stayed healthy. He's consistent. Basically, you got to average so many innings every time you get the ball. It shows that you're consistent. It shows that you're able to pitch deep in the game. It shows your stuff works not only on the first and second time through the order."
Alcantara was the first Marlins pitcher in 19 years, and fifth ever, with 200 K's in 200 innings. The others were Al Leiter in 1996, Kevin Brown in 1997, Ryan Dempster in 2000 and A.J. Burnett in 2002.
The Marlins will become Garcia's fifth team. The 30-year-old is coming off his best season, hitting 29 home runs with 86 RBIs -- both career bests -- for Milwaukee in 2021. Garcia opted for free agency earlier this month, and the Marlins have made it clear in recent weeks that landing outfield help was a top offseason priority.
Garcia has also played in Detroit, Tampa Bay and for the Chicago White Sox, a team he represented in the 2017 All-Star Game played at what was then called Marlins Park in Miami.
In parts of 10 seasons, Garcia has batted .270 with 127 home runs and 475 RBIs. He has played almost exclusively in right field, with limited time in center and left as well.
There is an obvious urgency to get the deals finalized, which will likely come early this week. A lockout is likely when baseball's labor contract expires Wednesday, and should that happen, it would be the sport's first work stoppage in 26 years.
Information from The Associated Press was used in this report.