The Liverpool legend will take control of the club this summer but has already started reshaping the club's squad.
Despite making his way through the youth ranks with the Scotland national team, Arfield represents Canada internationally, with his father having been born in Toronto. The 29-year-old has won 12 caps for his country.
“I am delighted to have added Scott Arfield to the squad for next season," Gerrard told the club's website.
"He is a talented and competitive midfielder who has competed at a high level in the English Premiership and internationally for Canada.
“It’s pleasing also that we have been able to start our rebuilding process so quickly after the end of the season. There is much more to be done of course as we look to build towards our Europa League campaign which will start in early July.
“Scott is the first one in and I look forward to working with him and the others who will be coming in to strengthen the squad.”
Burnley finished seventh in the Premier League this season, with Arfield scoring twice and laying on one assist in 18 top-flight appearances.