The former Fulham and Coventry City boss steps in to replace the late Gary Speed, who passed away in November, ahead of the country's 2014 World Cup qualification campaign
Previously the manager of Fulham and Coventry City, Coleman most recently spent a short time at Greek side Larissa, and now steps into the international role following the death of Gary Speed in November.
The selection of Speed's successor had been the subject of much debate, with Wales players such as Aaron Ramsey and Gareth Bale urging the FAW not to introduce major changes to Speed's successful set-up.
Dutch coach Raymond Verheijen, one of Speed's assistants, asked to be able to continue to work with fellow coach Osian Roberts and added that there was "no need for a new manager with new ideas".
In announcing the decision, the FAW explained that they had been keen to stay out of the public debate but had tried to take all points of view into consideration.
"This has been a very difficult process. We have explored every avenue, every scenario possible," Jonathan Ford of the FAW told reporters.
"We have taken on board the thoughts and views of the backroom staff, the players and the supporters.
"All along we believe that we have been respectful and dignified and had no wish to be involved in a public debate on the appointment of Gary's successor."
The FAW insisted that Coleman, who may work alongside Verheijen and Roberts, had been the ideal candidate to build on the foundations and legacy left by Speed.
"Gary was the manager of Welsh football and of course we want to continue his legacy.
"He was not a figurehead, he was the manager and that is why we have decided on the appointment of Chris Coleman to build on the excellent foundations put in place by Gary."