Bellamy has replaced Rob Page, who was sacked following Wales' failure to qualify for Euro 2024.
The 44-year-old former Liverpool, Newcastle and Wales striker leaves Burnley, where he was assistant to former manager Vincent Kompany last season in the Premier League.
"I will give my full commitment to develop this team and I am passionate to bring continued success into Welsh football," Bellamy told the FAW website.
"I can't wait to get started with our Nations League games in September."
Page guided Wales to their first World Cup in 64 years in 2022 and to the second round of Euro 2020 but failed to reach this year's Euros, losing in a penalty shoot-out to Poland in a play-off.
Page subsequently oversaw one of the most embarrassing results in Wales' history, a 0-0 draw with Gibraltar in a friendly and then suffered a 4-0 hammering at the hands of Slovakia.
Former Wales defender Page admitted following the Slovakian defeat he was in dangerous territory.
"They (Wales' fans) want me out. I completely understand. I've got to stay true to myself and focused on the job in hand. Everything else is out of my control," he said.
Wales' next game is the opening match of their Nations League campaign against Turkey on September 6, with a trip to Montenegro three days later.
