The Portuguese giants have paid around
£3m for the 18-year-old, who was nicknamed 'mini-Messi' by his team-mates at Tannadice Park.
Gauld, who has made one appearance for Scotland's Under-21s, scored eight goals in 38 games last season and had been linked with moves to Manchester United and Real Madrid.
However, Sporting have won the race for the attacking midfielder's services and he will now have the chance to emulate the likes of Luis Figo and Cristiano Ronaldo, who both played as youngsters in the Portuguese capital.
Dundee United said on their official website: "Everyone at the club wishes Ryan sincere best wishes in his future career."
