The 22-year-old had been on trial at Turf Moor, having left previous employers Aalesund in Norway after five years with the Tippeligaen outfit.
A central midfielder by trade, Ulvestad scored 18 goals in 122 appearances for his previous club and has also been capped by Norway at international level.
“He can cover a lot of ground, has nice skills with the ball and is at his best when he’s bringing the ball up the field at high pace.”
And Burnley have now moved to confirm that 22-year-old has put pen to paper on a deal with the club, announcing the news via the club’s official Twitter account.
Previously picked by Norway at Under-21 and Under-23 level, Ulvestad’s one appearance for the full national team came as a substitute in a friendly against the United Arab Emirates last year.
He will be hoping that regular appearances for Burnley this season will help him force his way into Per-Mathias Hogmo’s plans for the national side.
Currently third in their qualifying pool for the 2016 European Championships in France, Norway remain just a point behind leaders Croatia, who are ahead of Italy on goal difference alone.
Impress in the Premier League and Ulvestad could prove to be a valuable asset for Hogmo ahead of what is likely to be a tricky remaining set of international fixtures.