Claire Valoti, who was recently promoted from UK general manager to be vice-president of international sales at the Snapchat owner, previously worked with Couchman at Facebook.
Couchman, the director of agency partnerships at Facebook in the UK, has worked at the social media giant for six years. He will start at Snap in June.
Facebook is expected to replace Couchman but members of the agency team will cover his duties for an interim period.
Valoti and Couchman previously worked together at Facebook where they were joint directors of agency relations.
He took sole charge after she quit for Snapchat at the end of 2015 to be its first UK general manager.
Snap has grown from five to 140 employees in the UK since Valoti joined and the London-based operation says it doubled revenues in 2017.
Emarketer has estimated Snap’s UK revenues grew from £22m in 2016 to £53m in 2017 and it forecasts further growth to £105m in 2018 and £310m by 2020 when it could overtake Twitter.
Valoti said: "Ed is the right person to take the business to the next level. He has a proven track record of building strong relationships within the media and advertising industry and his appointment underscores our continued commitment to our agency partners in the UK."
Couchman was previously head of digital and future media at Channel 4 before joining Facebook.
He said: "Snap has scaled incredibly quickly in the UK and I look forward to building on the success of Claire and the UK team.
"Snapchat’s efforts to remove friction from visual communication have resulted in a highly engaged, mobile-first audience.
"It will be great working with advertisers to figure out how it fits into their overall marketing and communications strategy and delivers the business results they need."
Steve Hatch, vice-president of Facebook, northern Europe, thanked Couchman for "his dedication and contribution to the business over the last six years".
Facebook has had a stellar run since 2012 when it launched on the US stock market but it is now facing a political storm after admitting up to 87 million users’ details may have been used by Cambridge Analytica, the British data firm which worked with the Trump and Brexit campaigns.
Snap faces different pressures after disappointing investors since its debut on the US stock market in March 2017.
The share price has halved since the IPO but has made up some ground since the start of 2018. Snap reportedly cut more than 100 jobs globally earlier this year.
Valoti was promoted in February after Jeff Lucas departed as vice-president of sales.
Snap is on a mission to increase international sales, which made up 23% of global turnover in 2017 compared to 12% in 2016.
Valoti oversees sales offices in the UK, France, Germany, the Netherlands, Sweden, Norway, UAE, Canada and Australia.