The person spoke to the AP on condition of anonymity Saturday because the agreements are pending physicals by the players and have not been announced.
Hill, a 40-year-old left-hander who has pitched for nine others teams over portions of 16 major league seasons, agreed to a deal worth $2.5 million. He is 67-44 with a 3.79 career ERA in stints with the Los Angeles Dodgers, Chicago Cubs, Baltimore Orioles, Boston Red Sox, Cleveland Indians, Los Angeles Angels, New York Yankees, Oakland Athletics and Minnesota Twins.
The starter went 30-16 with a 3.16 ERA from 2016-2019 with the Dodgers and was 2-2 with a 3.03 ERA with the Twins during the 2020 pandemic-shortened season.
McHugh, 33, has been both a starter and reliever during parts of eight seasons with the New York Mets, Colorado Rockies and Houston Astros, going 58-43 with a 3.95 ERA. The right-hander signed with Boston in 2020 but opted out of the shortened season while recovering from an injury.
Hill and McHugh are the latest additions to a pitching staff that Tampa Bay is revamping after winning the AL pennant last season.
The team declined an option on right-hander Charlie Morton and traded 2018 AL Cy Young Award winner Blake Snell, creating openings in the rotation that offseason signees Michael Wacha and Chris Archer will have an opportunity to fill.
Hill and McHugh potentially add depth to both the rotation and bullpen.