The club announced the deal Friday.
The 23-year-old centre played in 74 games last season with the Rangers' Hartford affiliate last year in the American Hockey League. He had 21 goals and 16 assists, and posted a plus-16 rating. Bourque set career-highs in games played, goals, assists, plus/minus, power play goals (seven), game-winning goals (three), and shots (158).
In 196 career AHL games in three seasons with Hartford, Bourque has 35 goals and 31 assists. His goal and point totals have increased each season since his rookie campaign in 2011-12.
Bourque, chosen by the Rangers in the third round of the 2009 draft, has yet to make his NHL debut.