Go Ahead won the home leg 3-0 in midweek, meaning they could afford to lose 1-0 in the return, Jack Tuyp with the only goal after 15 minutes.
The result caps a fairytale run through the play-offs for a club who only finished sixth at the end of the regular Eerste Divisie season.
Go Ahead, champions of Holland four times in the days before the advent of the professional game in the country in 1954, can now look forward to top-flight football for the first time since finishing bottom of the Eredivisie in the 1995/96 season.
For their part, Volendam will be glad to see the back the Deventer club, who beat them 3-1 on the final final day of the season to allow Cambuur Leeuwarden to snatch the title from their grasp.
In the day's other tie, Roda JC ensured they will live to fight another day in the Eredivisie after a Mark-Jan Fledderus double gave them a 2-1 win over Sparta Rotterdam.
After a goalless first leg, the top-flight side made life hard for themselves after falling behind to Mario Bilate's 24th-minute strike, but Roda fought back late on, Fledderus equalising after 73 minutes before scoring the winner with seconds remaining.
In the play-off for Europa League qualification, FC Utrecht survived a second-leg fightback to wrap up a 3-2 aggregate win over FC Twente.
Utrecht took a stranglehold on the tie by winning the away leg 2-0 in midweek, but were made to sweat as goals by Dusan Tadic (34) and Nacer Chadli (36) saw Twente to a 2-1 win in today's return leg.
Edouard Duplan, also on target in midweek, hit the crucial goal a minute after the restart for Utrecht, whose prize is a place in the second qualifying round for next season's Europa League.