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Berrington, 35, is Scotland's most-capped player in ODI and T20I cricket and has occasionally deputised for Coetzer, most recently against Namibia at last year's T20 World Cup.
His first assignment in the full-time role is a tri-series against Namibia and Nepal from July 10-17, which forms part of the Cricket World Cup League 2. Matthew Cross, the wicketkeeper-batter, will be his vice captain.
"I feel incredibly honoured and privileged to lead this team and represent my country," Berrington said in a press release. "Having come through the Scottish system from a young age, I'm very proud to take on the role of men's captain.
"As a team we're very much looking forward to what's ahead - three home series over the next couple of months is a great opportunity for us to keep building on the team's recent success and we'll be doing all we can to produce some good results in front of a home crowd.
"We've had a fantastic leader in Kyle, who has been a great ambassador for our sport and I have learnt a lot under his leadership. [In the] long term, World Cup qualification is key for us and we are determined to keep pushing towards full member status, while continuing to develop the younger players we have coming through."
Shane Burger, Scotland's coach, said: "I have no doubt that Richie will lead the Scottish men's side with distinction and is the right person for the job. His stature not only in the Scottish game, but world cricket, makes him a fitting appointment - we have a leader in Richie that everyone can be proud of."
Coetzer has retained his place in the 14-man squad for next month's tri-series having stepped down from the captaincy earlier this month.
Scotland squad for Nepal and Namibia tri-series: Richie Berrington (captain), Matthew Cross (vice-captain, wk), Kyle Coetzer, Calum Macleod, George Munsey, Dylan Budge, Mark Watt, Safyaan Sharif, Michael Leask, Gavin Main, Adrian Neill, Hamza Tahir, Chris Sole, Chris McBride