McKenzie is available for Saturday's game against the Ospreys, while Toolis has joined on a short-term loan.
Heriot's back-rower Jason Hill, who scored for the Scotland Club XV in the recent win over Ireland, has also been training with the squad.
Glasgow Warriors head coach Gregor Townsend said: "We'd like to thank Edinburgh Rugby for loaning us Fraser (McKenzie) and Alex (Toolis) and we're also very grateful to Heriot's.
"It's a great opportunity for Jason (Hill) to train with us and we look forward to involving him more during the season."We'd like to welcome all three players to the club."