The 23-year-old makes the move to Belle Vue, having ironically played against manager Dave Penney's side in last season's Conference play-off final, when he was on loan to Dagenham & Redbridge.
The former Republic of Ireland Under-21 international made just three substitute appearances in The Premiership for Villa before being let go in mid-May by the West Midlands giants.
McGrath will hope his move to Donny provides him with plenty of first team action, as the club look for a successful return back in The Football League.
Meanwhile, the club have announced that they will not be running a youth side this coming season after receiving news that the PFA will not fund scholarships for sides playing their first season back in the league.
Donny intend to re-instate their youth team the following season, once the eligibility of funding is available from the PFA for season 2004/05.
Penney is disappointed that the club have had to make this decision but plans on providing short-term opportunities to its current youth team players for next season.
"Obviously I'm disappointed and although we will continue to look at lads throughout the season, we will be unable to set them on until we reactivate the youth team next season," Penney told the club's official website.
"It is a shame that The Football League have told us to abide by their rules on this but don't offer any financial support.
"What we are doing is honouring the contracts of any youth players already here and they will play in the reserves next season.
"We are also looking at gaining them experience by loaning them out to other clubs in the Conference and Unibond (League) to give them a better football education."
