Boyd, 20, has signed a four-year contract with Vitoria, which is fifth midway though this season's Portugal Primeira Liga.
A five-cap New Zealand international, Boyd was in the first intake of Phoenix's school of excellence development program before signing a three-year contract.
He has scored four goals in 47 appearances for the club, most of which were as a substitute in his first season.
Boyd started nine of his 20 games in 2013-2014 but his involvement this season has comprised just four bench appearances. He scored twice late in a 3-1 win away to Adelaide United on New Year's Eve.
Phoenix coach Ernie Merrick understood Boyd's desire to move overseas at the end of the season.
"We have known for some time that Tyler wanted to play in Europe and I wish him all the best for the future," Merrick said.