The Scottish Football Association said the 39-year-old Belgian had signed an initial two-year contract and would lead Scotland into the forthcoming UEFA Nations League campaign.
Former Union Saint-Gilloise and Monaco head coach Pocognoli replaces Clarke, who resigned as Scotland boss following the team's group-stage elimination at the World Cup in June.
Pocognoli, a former Belgium international, led Union to the 2024/25 Belgian title in his first season as a head coach.
He described his appointment as an "honour" and added on the SFA website: "When I first heard of the interest, I was immediately excited about the opportunity.
"Scotland's supporters are famous for their passion - most recently at the World Cup in the USA - and I have experienced it myself as a player for Belgium when we played in 2013.
"Along with my coaching staff, I will do everything I can to give them a team to be proud of and build on the success that has been achieved already by my predecessor."