The duo helped guide the club to their fourth league title last year following Tandy's appointment in February, which was following by Rees's arrival two weeks later.
Chief operations officer Andrew Hore told the club's official website: "Steve and Gruff are two of the brightest, most exciting young coaches around and have already developed excellent reputations as innovative, forward thinkers.
"Products of the well established coach development pathway we have in place here at the Ospreys, they have both worked extremely hard to help put foundations in place over the last 15 months to help ensure a sustainable, long term future for the region."
Tandy added: "I'm extremely happy to sign this new contract and I'm really looking forward to the future with this group of players. We've got a great base to work from, with an experienced core of real quality international players and British Lions, and some outstanding young talent that has come to the fore over the course of this season.
Rees also expressed his delight with his new deal.
"I'm extremely grateful to both the Ospreys and Steve for the confidence shown in me and these contract extensions allow us the opportunity to continue working together towards our aim of long-term sustainable success," he said.
Meanwhile, the team are preparing for Friday night's final day RaboDirect PRO12 clash with Leinster in Dublin.