Beggs, 28, posted a 1-0 record and a 4.15 ERA with 20 strikeouts in 26.0 innings of work in five games, all of which were starts, with Lexington.
MLB has purchased 53 Atlantic League contracts.
The Mets originally drafted Nate Peden in the 13th round of the 2017 MLB June Amateur Draft out of University High School in Orlando, Florida.
Hoover joins former Reds teammates Brandon Phillips (player/part owner), Tony Cingrani, and Jordan Pacheco on the Lexington squad.
In a historic move, Phillips will join Lexington as the first-ever Atlantic League player to be on the roster for a team that he co-owns.
While with the Mets, the Bronx-born Rivera posted a .304 batting average, eight homers, 43 RBI, 37 runs, 17 doubles, two triples, and a .335 on-base percentage. He also laced a double during the Wild Card playoff game against the San Francisco Giants.
Fields slugged 14 longballs, 36 RBI, 44 runs, 10 doubles and 11 stolen bases in 89 games with Long Island during the 2019 campaign.
Florence won the championship that the Legends hosted postseason, per Lexington team source.
Alfonzo--whose dad, Edgar Alfonzo, managed in New York's minor league system--played 75 contest with the Columbia Fireflies, a Mets' Single-A affiliate in 2018.
The Mariners picked Pizzano in the 15th round in 2012, while the Yankees selected Scott in the 14th round of the 2016 Draft.