US Marine Corps crew chief Corporal Spencer Collart, 21, pilot Captain Eleanor LeBeau, 29, and Major Tobin Lewis, 37, died in the incident, the US military said.
The US president, Joe Biden, and the Australian prime minister, Anthony Albanese, extended their condolences to the families of those killed.
All 20 survivors were injured and were flown by rescue aircraft to hospital in Darwin.
Three remained in hospital on Tuesday, one in critical condition and two stable, a Marines statement said.
An investigation is taking place into the cause of the crash.
Up to 2,500 US Marines have been based in Darwin for six months a year since 2012 as part of the US military pivot to Asia to counter China's growing influence in the region.
Col Brendan Sullivan, the commanding officer of the Marine Rotation Force-Darwin, said the Marines' focus was on supporting the recovery of wreckage and investigating the cause.
"We are deeply saddened by the loss of three respected and beloved members of the MRF-D family," Sullivan said in a statement.
"Our thoughts and prayers remain with the families and with all involved," Sullivan added.
The Osprey is a hybrid aircraft that takes off and lands like a helicopter but during flight can tilt its propellers forward and cruise much faster like an airplane.
Before Sunday, there had been five fatal crashes of Marine Ospreys since 2012, causing a total of 16 deaths.
Three Marines were killed when an Osprey plunged into the Coral Sea off Australia's northeast coast in 2017. The remaining 23 people on board were rescued.