Ospreys Coach Lyn Jones said, "We are an ambitious region and bringing in players such as these develops a level of competition within the squad that will help to keep everyone at the top of their game."
Wales scrum half Phillips, 24, has signed a £180,000-a-year deal to switch from Cardiff Blues to the Ospreys where he will compete with Justin Marshall to form a dream partnership with James Hook.
Jones said, "Mike and Justin have had some enthralling battles this season and I look forward to seeing their contest for the Ospreys number nine shirt. They are both highly competitive individuals and neither will want to play second fiddle."
Lock Gough, 30, will leave the Dragons after making more than 230 appearances for the Rodney Parade club, though is not expected to play until November, after the Rugby World Cup.
Jones added, "Ian has an excellent technical game and this, combined with his physical presence, will offer a standard of performance that no one will afford to drop under. The group of players we have in this boiler-house next season will be second to none."
The Ospreys have also signed Mark Taylor from Sale Sharks as well as securing Hook, Marshall, Gavin Henson and Shane Williams to long-term contracts.