Tilio has agreed a five-year deal at Celtic Park and becomes the second signing of Brendan Rodgers' second spell at the club after the arrival of Norwegian midfielder Odin Thiago Holm (20).
Tilio, who has seven international caps, scored 20 goals in 82 games for Melbourne.
"I'm ecstatic that I'm coming over to Europe, coming to such a big club and team, and I'm super-excited," Tilio told Celtic TV.
"It's an amazing opportunity for myself and having seen Aussies go over there and do well at such a prestigious club, it's a massive opportunity for myself that I couldn't deny."
Tilio will not be joining his former international teammate Aaron Mooy (32) at Celtic Park after the midfielder announced his retirement on Friday.
However, his path to the first team under Rodgers could be eased by the departure of Portuguese winger Jota (24), who has been linked with a move to Saudi club Al-Ittihad.