He becomes Wales' third Kiwi coach of rugby's professional era, following Graham Henry and Steve Hansen.
Gatland, who led Wasps to a hat-trick of Premiership titles from 2003 to 2005 and landed Heineken Cup glory with the Londoners in 2004, succeeds Gareth Jenkins.
Jenkins stood down in September following a poor World Cup campaign when Wales failed to progress beyond the pool stage, losing their final game against Fiji in Nantes.
Jenkins' World Cup assistant Nigel Davies will take charge for the one-off Test against world champions South Africa in Cardiff on November 24.
Gatland said: "This is a great honour and I feel a tremendous sense of pride in having been chosen as the new head coach of Wales.
"I've been given the opportunity to coach at the highest level and I am very grateful to get this chance.
"There is a lot of hard work ahead but I know there is enormous talent in Wales and I feel extremely positive about what can be achieved.
"My aim is to leave Welsh rugby in a much better state when I finish here than it is at the start of my career as Wales coach.
"I want that success to be based on strong foundations and I will be seeking to work closely with the regional coaches to achieve my aims.
"There's a huge amount of potential here to take the game forward and the regional sides in Wales are now beginning to get better and better."
Gatland will return to New Zealand after the weekend and will be back in Wales from early in December to take up his new role full time.
He added: "The coaching team in charge for the South Africa game must be allowed to have their opportunity and the preparations for that match are now well advanced."
He was recruited to the Wales job after a worldwide search by a three man Welsh Rugby Union panel of group chief executive, Roger Lewis, Chairman David Pickering and WRU Board member Gerald Davies, the former Wales and British and Irish Lions wing.
Lewis said: "We are delighted to have secured our first choice candidate as the new Head Coach of Wales.
"It was clear from our first meetings with Warren that he has the capability, attitude and integrity to deliver for Wales.
"His achievements so far as a player and coach speak for themselves and he undoubtedly possesses a burning desire for success."