General manager Jeff Gorton announced the signings on Wednesday. Contract terms were not immediately available.
The signings leave only Derek Stepan as the major unsigned restricted free agent with the Rangers, who posted the best regular-season NHL record before losing in the Eastern Conference finals to the Tampa Bay Lightning.
Fast and Miller both played well in the postseason, when Fast had three goals and three assists in 19 games and Miller had a goal and seven assists.
Miller had 10 goals and 13 assists in 58 games with the Rangers this past season. He established NHL career-highs in games played, goals, assists, game-winning goals (three), power play goals (two), and power play points (three). Miller tied for fifth on the Rangers in game-winning goals and ranked sixth in shooting percentage (10.9 percent).
The 22-year-old Miller registered eight points (three goals, five assists) in the final 13 games of the regular season.
Miller has skated in 114 career NHL games over parts of three seasons, with 15 goals and 18 assists.
Fast played in 58 games with the Rangers this past season, with six goals and eight assists. From the time he was recalled from Hartford on Nov. 10, the team earned at least one point in 42 of the 55 games he played. The 23-year-old was selected by the Rangers in the sixth round of the 2010 NHL entry draft.
Earlier in the day, the Rangers signed restricted free agent defenseman Dylan McIlrath, who has spent most of the last five seasons with the Hartford Wolf Pack (AHL).
McIlrath had six goals and 11 assists in 73 games with the Hartford Wolf Pack (AHL) last season. He skated in one game with the Rangers last season.