Defender Anthony is the club's longest-serving player having made his debut in September 2007, scoring against Nottingham Forest, but the 27-year-old concluded the current campaign on loan at Hereford.
McGleish, 38, was also a loanee at Barnet in the closing months of the season. The well-travelled striker scored seven times in 18 starts for Rovers after joining on a free transfer from Leyton Orient.
Charlie Reece, Charlie Clough, Lance Cronin and Michael Boateng will also leave the club.
Kayne McLaggon has not been offered a new deal alongside Wayne Brown, Danny Woodards and Jim Paterson, but will train with the club until he returns to full fitness. Elliot Richard and Ollie Clarke have already accepted offers to stay with Rovers.
Lamar Powell, Darren Jefferies and James Dale exit at the end of their two-year scholarships, although fellow scholars Jordan Goddard, Mitch Harding, Ellis Harrison and Ross Staley have been offered professional terms.