On July 12, the Old Trafford team will face Jurgen Klopp's Liverpool at the Rajamangala stadium in Bangkok.
On July 15, they will face Melbourne Victory at the 100,000-seat Melbourne Cricket Ground, followed by a match against Palace on July 19 at the same location.
Because of Covid-19, clubs have not been on pre-season tours in recent years.
Manchester United chief operating officer Collette Roche said, "It's been two years since the club has been allowed to travel on an international pre-season tour, so we can't wait to get underway this summer and reconnect with our fans in south-east Asia and Australasia."
Manchester United's football director, John Murtough, stated the club's summer tour will include "great training facilities and high-quality opposition."
After the resignation of Ole Gunnar Solskjaer, the club could have a new manager in place by the time of the tour. Head coach Ralf Rangnick is presently in interim command.
Steve Parish, chairman of Crystal Palace, said: "For the first time in the club's history, we are ecstatic to be touring Australia.
"Even more so after Covid forced us to postpone two planned trips in recent pre-seasons.
"It will be incredible to see Crystal Palace play in Australia for the first time, and to do so at the legendary MCG in front of our Australian fans and strong travelling support is something the entire squad and staff, lead by Patrick Vieira, are looking forward to."
