Cox will be familiar to Warriors supporters, having graduated from the club's academy in 2007 before spending three years as a first-team player.
The 25-year-old moved to Gloucester in 2010 and has gone on to make 58 appearances for the Cherry and Whites.
He was instrumental as Gloucester won the LV= Cup in 2011 and has helped his current side secure a Heineken Cup position for two of the last three seasons.
On the international front, the Redditch-born forward represented England at Under 18 and 19 levels before starring for the Under 20s during the successful 2008 Six Nations campaign. He has also played sevens for his country.
Cox said: "When Dean approached me and told me about his plans for my hometown club, I knew it was something I wanted to be part of.
"I've worked closely with Carl at Gloucester and with those two at the helm, I believe the club will be successful in the future.
"With the likes of Chris Pennell and Alex Grove committing to the club, it is clear to see how much potential there is."
Cox will be joined at Sixways by team-mate Mills, who will make the short journey north after four years at Kingsholm.
The centre, who can also play at fly-half, has scored 35 points in 20 games for Nigel Davies' side since graduating from Hartpury College.
He previously spent 12 years with Exeter Chiefs from the age of five before cementing a place in the England Under 18 and Under 20 squads.
Mills was part of the Under 20 Junior World Cup and Six Nations squads in 2011 and 2012, helping his country to Grand Slam success in the latter three years ago.
Mills said: "I have thoroughly enjoyed my time at Gloucester. It's been unfortunate, however, that I haven't played as much as I would have liked due to a number of injuries.
"The opportunity to join Worcester was one I was keen to take. I am extremely excited to link-up with Dean Ryan and Carl Hogg and can't wait to join the club on their journey ahead."
Director of Rugby Ryan stated: "It is an extremely positive development for the club to secure the services of in-demand players such as Matt and Ryan who have made the choice to join us at Sixways."
Chief Executive Charles Cameron added: "I am delighted that Matt and Ryan will be joining Warriors and it again illustrates our commitment to bring success to this club."