The Belgian club announced on Monday they had given the 23-year-old international permission to travel to Spain to complete his transfer for an undisclosed fee.
A statement from Club Brugge read: “Mathew Ryan is travelling today to Valencia to undergo a medical before his transfer is completed.”
Valencia are keen to strengthen at the back with first-choice goalkeeper Diego Alves sidelined until next year with a knee injury.
Manchester United keeper Victor Valdes had been strongly linked to Valencia in recent weeks but the former Barcelona player was considered too expensive.
Ryan, who was a reported target of Liverpool last year, confirmed his impending departure on the club’s official website.
He said: “If I pass a medical, I will indeed leave the club.
“It was a pleasure to be a part of this club.
“This club went out of their way to keep me for an extra year, which made the choice even more difficult.”
Ryan joined Brugge in May 2013 from Central Coast Mariners and was under contract for another three seasons.
He was twice selected by the Belgium Pro League as goalkeeper of the year.
“I’ve had a great time here,” Ryan said. “But I feel that it is time to take another step.
“Last year I blew a nice offer but this time I really could not refuse.
” I am grateful for the opportunities that the club has given me, as a young player I could imagine no better place to grow.”
Valencia finished fourth in La Liga in the 2014-15 campaign and will play in next season’s Champions League.