Rennie will see out the current Guinness PRO14 season with the Scotstoun side while Wilson will continue to work with the national team until the end of the 2020 Six Nations championship.
The 43-year-old cut his teeth on the coaching circuit with spells as Forwards Coach with Welsh sides Dragons and Scarlets bnetween 2010 and 2014, and coached the Wales Under-20 team during the same period.
Wilson spent a season as Forwards Coach with Bristol, working under former Scotland head coach Andy Robinson, before a successful three-year stint as head coach of Cardiff Blues.
He guided the Welsh side to European Challenge Cup glory in Bilbao as well as securing a return to the Heineken Champions Cup, before joining the Scotland set-up under Gregor Townsend in August 2018.
Dodson: Wilson an 'excellent coach retained within Scottish professional game'
Scottish Rugby chief executive Mark Dodson welcomed the appointment of Wilson, saying: "We are very pleased Danny has accepted this important role at Glasgow Warriors as it retains an excellent coach within the Scottish professional game.
“Danny has worked hard to develop Scotland’s set-piece into a real area of strength and his technical expertise, aligned with his working knowledge of many of the Warriors’ players, will be key to maintain the club’s progression in the coming years.
“He has a depth of experience from previous roles with PRO14 teams and we feel this, alongside his recent international coaching, makes him the right person for the club at this time.
“I’d like to thank Danny for his contribution to the Scotland team and wish him well as we continue our ambitious plans to make both Glasgow Warriors and Edinburgh as competitive and successful as possible in their respective competitions.”
Wilson: 'Too good an opportunity to miss'
Wilson added: "The opportunity to coach such an attractive club as Glasgow Warriors was too good to miss.
“I’ve been extremely impressed with Scottish system in recent years and I’m looking forward to working with an exciting and talented squad of players at Warriors.
“I want to build on the high-tempo style of play that I know the fans love and pay to see week in, week out.
“The club has been challenging at the top end of the Guinness PRO14 on a regular basis and as a coach it is that type of environment and culture you want to be involved in.
“I took a huge amount of learnings from the time I have spent with Scotland through the Guinness Six Nations and Rugby World Cup and I’m thankful for that experience, which can only add to how I take on a new Head Coach role with Glasgow.”