Callahan will wear No. 43, that Addison Reed previously wore, and Rhame will wear No. 35. Both will be on major league rosters for the first time.
Callahan, 23, came to the Mets from the Boston Red Sox as part of the deal for Addison Reed. Callahan has allowed two runs on 12 hits, four walks and ten strikeouts in 10 innings since the trade for the Las Vegas 51s.
Overall this season, Callahan has a 2.94 ERA, 1.25 WHIP, seven saves and 66 strikeouts compared to 17 walks in 52 innings.
The former second round pick has to be added to the Mets 40-man roster. He features a three pitch mix of a 94-98 MPH fastball, splitter and slider.
Rhame, 24, was the Mets return when they traded Curtis Granderson to the Los Angeles Dodgers. He has allowed only one run in six innings on two hits, zero walks and 11 strikeouts since joining the 51s.
In Triple-A this season, Rhame has an 4.00 ERA, 1.19 WHIP, 66 strikeouts and 10 walks in 54 innings.
He is already on the Mets 40-man roster. Rhame brings a high octane fastball in the 94-100 MPH range, two-seamer, hard slider and an occasional splitter.
MLB Pipeline has Callahan ranked as the Mets No. 23 prospect and Rhame at No. 30 in the organization.