Striker Elliott, 24, arrives on a free transfer from Cambridge and 27-year-old defender Osborne has agreed a season-long loan from Bristol City.
Boss Neal Ardley told the Dons’ website: “We’ve signed Karleigh on a season-long loan, with no breaks, he’s ours for the season until May 31.
“I’d like to thank Bristol City and Steve Cotterill in particular who have been great through the whole process.
“We’ve got a player who has played a lot of League One games, played Championship, he’s strong, athletic and powerful and he ticks the criteria that we tried to set at the start of the summer and we’ve been patient to land.
“I met with Tom probably over a month ago now and sold the deal to him. He went away and there was a lot of interest from other clubs, to the point where he had an offer from a League One club and I thought we’d lose him, but we’ve managed to seal the deal.”