Both Lewsey and Easterby have worked with Gatland in previous jobs.
Lewsey was an integral part of the Wasps side that won three successive Premiership titles under Gatland from 2003 and 2005, while also landing the Heineken Cup in 2004.
Llanelli Scarlets captain Easterby made his Test debut when Gatland coached Ireland, before linking up with Wasps.
Lewsey said: "The players will have a fantastic time working under Warren, and no doubt their success will speak for itself.
"I think this is one of the best appointments for a northern hemisphere team - and I am sure that in the very near future we will see a resurgence of the sleeping giant that is Welsh rugby."
Easterby added: "I am not surprised Wales have gone for him.
"I only worked with him for a short period, but his track record speaks for itself in terms of winning trophies.
"I got my first cap under Warren. He gained a lot of respect from the players - he was very diligent in his preparation and got his job done.
"He was the start of Ireland's resurgence in terms of results and the team we have had for the past six or seven years."
Gatland, 44, will officially take charge on December 1.
His reign - assuming he lasts the distance - will incorporate Wales' 2011 World Cup challenge in his native country.
Gatland succeeds Gareth Jenkins, who was sacked following Wales' dismal World Cup campaign when they failed to progress beyond the pool stage.
The opening game of Gatland's tenure will be against World Cup finalists England at Twickenham on February 2, when this season's RBS 6 Nations Championship kicks off.
Gatland said: "I am totally committed to doing the best job I can, and to put a team out that I hope the Welsh public will be proud of.
"I know the pressures and expectations that are going to be placed on me in terms of the role I have been given.
"But this was an opportunity and a challenge I couldn't walk away from. As a coach, you always want to coach at the highest level, and I have got that chance again.
"There will be some ups and downs - I hope more ups than downs - and we can move things forward.
"I am asking people not to expect miracles from day one. It is going to take a little bit of time, putting things in place.
"Being 10th in the world is too low a ranking, and I intend to try and improve that.
"We all want to see some consistency, not a rollercoaster ride, and consistency is a real key for me."
If Wales great Gerald Davies - part of the three-man Welsh Rugby Union team that secured Gatland's services - has his way, that consistency will also apply off the field.
Wales have had five coaches in the past five years, which represents a wholly unsatisfactory situation as far as WRU board member Davies is concerned.
He said: "It should be one of our ambitions as a union to stop this revolving door, where we have a coach coming in one year, only to exit pretty quickly the following year or the year after that."