Queensland Reds back Johnson and Leicester lock Peterson have penned two-year deals with the Guinness Pro12 leaders, subject to visas and medicals.
Johnson, 21, played both union and league before joining Reds in 2013 and has made two Super Rugby appearances since being promoted to their first-team squad last year.
Looking ahead to joining up with Gregor Townsend’s side, he said: “I’m excited about working with the coaches at Glasgow and I’ve heard a lot of good things about the club and the city.
“Glasgow play free-flowing rugby and I really like the way they attack, which is a bit different to typical European teams and defensively their structure is second to none.
“I’ve been watching the European Rugby Champions Cup this season and I’m looking forward to having the opportunity to test myself at that level against some of the best teams in the world.”
Peterson, 24, was born in Australia but qualifies for the USA courtesy of his American grandfather and will help bolster the pack’s engine room, with Warriors skipper Al Kellock retiring to take up an ambassadorial role in the summer.
He was with the New South Wales Waratahs for five years after joining their Academy in 2009, and has made one Super Rugby appearance.
The towering forward has three caps for the United States and has also represented Australia Under-20s.
Peterson comes from a rich athletic background, his father having played American Football for Northwestern University in Chicago and his grandfather having played in one of the first ever rugby union games in the United States.
Peterson said: “Gregor has given me the opportunity to join Glasgow and I believe I can help the team progress further.
“I’ve learned a lot at Leicester about northern hemisphere rugby and I’ve loved my time there. I’ve always given 100 per cent and I’ll do the same for Glasgow.
“I like the style of rugby Glasgow play and everybody works hard for each other, which is how I think the game should be played.
“Talking to Gregor about the values of the team and the way the team plays almost feels like a perfect fit, so when I get up there I’ll grab the opportunity with both hands and show the supporters the kind of player I am.”
Townsend added: “Both Sam and Greg will be great additions to our squad next season and we’re looking forward to them joining us.
“Sam has played very well since his return from rugby league. He has been a regular for the Reds’ back-up side this season and his impressive performances have seen him break into the first team.
“He is a strong-running ball carrier that can cover both centre positions and we believe that he will continue to improve within our environment.
“Greg has picked up some great experience already in his rugby career and played well for the USA in the November Tests. He is determined to make the most of his opportunity with us.
“He has a real physical presence and hits hard in the tackle. He will give us something different and add to the competition for places in the second row.”
The signings are the latest developments in a significant rebuild at Scotstoun ahead of next season. Veteran hooker Dougie Hall is joining Kellock in retiring, while Fijian fans’ favourite Niko Matawalu, record try-scorer DTH van der Merwe and Lions back Sean Maitland will all depart Glasgow at the end of this brilliant, and potentially historic, Guinness Pro12 campaign.
Johnson and Peterson join former Scotland captain Mike Blair and Italy flanker Simone Favaro in the squad for next season, while moves have been made to retain the services of key players Stuart Hogg, Tommy Seymour, Henry Pyrgos, Josh Strauss, Leone Nakarawa, Adam Ashe, Lee Jones and Peter Horne.
Meanwhile, Glasgow Warriors are holding a charity auction to raise funds in support of the Glasgow School of Art Development Trust’s appeal for £20 million to assist recovery from the devastating fire in the iconic Mackintosh building last May.
The auction, which is partnered by one of the club’s new official sponsors, McTear’s Auctioneers, will include a number of signed Glasgow jerseys and is now running at www.mctears.co.uk/live until Sunday 17 May.