Scrum-half Phillips moves from Cardiff Blues on a four-year contract believed to be worth around Â£700,000, while Newport Gwent Dragons lock Gough has secured a three-year deal.
Phillips, who has won 17 caps, will go straight into a head-to-head battle for the Ospreys number nine shirt with former All Blacks star Justin Marshall.
Marshall recently agreed a two-year contract extension at the Liberty Stadium, and was involved in a players' tunnel pushing match with Phillips following the Ospreys' EDF Energy Cup semi-final victory over Cardiff last month.
Ospreys head coach Lyn 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, although somewhat at differing ends of their careers, and neither will want to play second fiddle.
"But they are good professionals, and I anticipate the squad will be foremost in their thoughts.
"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."
Gough, capped 35 times, moves from the Dragons, where he has established himself as a consistent performer, and he will increase the Ospreys' second-row firepower alongside players such as Alun Wyn Jones, Ian Evans and Brent Cockbain.
Jones added: "Ian has an excellent technical game, and this, combined with his physical presence, will offer a standard of performance no-one can afford to drop under.
"With regular demands at international level throughout the season, it is important key positions are well-staffed, and the group of players we have in this boiler-house next season will be second to none. "
Ospreys rugby director Kevin Hopkins claims the Swansea-based region fought off significant rival interest in Phillips and Gough.
Hopkins said: "These players have seen how the region has developed and were keen to commit themselves to the Ospreys.
"We have fought off serious competition from outside Wales to secure the services of Ian and Mike, and it is great news for everyone in Welsh rugby that these players are now retained within the Principality."