The 22-year-old Norway international decided against renewing terms with the Tippeligaen outfit and has agreed a switch to Turf Moor, subject to clearance.
Ulvestad joins a side battling relegation from the Premier League, with manager Sean Dyche hopeful his new signing will adjust to life in the English top flight.
"Fredrik is someone who came into the club to spend some time with us earlier this year," Dyche told Burnley's official website.
"We liked what we saw and he has gained some good experience playing in the league in Norway.
"It's a new challenge for him now, not only on the pitch but off it too in terms of culture.
"He has gained a full international cap and is learning and gaining experience all the time. We will be looking for him to continue his development and improve further as a midfielder.
"There will be an adjustment period, for sure, because of the change in the levels of football.
"We know how tough the Premier League is, so he will be given time to adjust to that accordingly and continue his development."
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