The deal with Ristolainen, the No. 8 pick, was announced Friday night.
Ristolainen was the first of two defencemen selected by the Sabres in the first round. Russian prospect Nikita Zadorov was taken with the No. 16 choice.
Ristolainen, a 6-foot-4, 225-pound Finnish prospect, has been participating at Buffalo's development camp and is expected to compete for a roster spot with the Sabres next season.
He had three goals, 12 assists, and 32 penalty minutes in 52 games with Finland's TPS this past season.