Gatland has said he rejected an approach from Super Rugby side Chiefs about leading them from 2018.
Gatland is contracted with Wales until after the 2019 World Cup in Japan.
Phillips reinforced his belief Gatland will return, saying he "made it very clear his intention was to come back".
The WRU boss also does not expect any fall-out from the Lions tour that would affect the Wales camp.
After Gatland's Wales and Lions predecessor Graham Henry took the Lions to Australia in 2001, his relationship with senior Wales players suffered.
"The reason Warren has got the Lions job twice and assistant once is that he is a very experienced leader in that space," Phillips told Scrum V.
"So I would back him to manage the situation."
Phillips also defended the decision to allow Rob Howley to join Gatland as part of the Lions set-up.
Forwards coach Robin McBryde will be in charge of Wales' June tour Tests against Tonga and Samoa, assisted by regional coaches Danny Wilson, Matt Sherratt, both of Cardiff Blues and Scarlets' Stephen Jones.
"I think Warren and Rob will both benefit as coaches from the Lions experience," added Phillips.
"I don't think the South Sea Island tours will be hugely beneficial to them.
"Our belief was for Warren and Rob to go into the white-hot heat of a Lions tour will test and develop them.
"We genuinely have to give some coaches exposure so I am comfortable with that decision."
Phillips also defended the 2016 decision to award contracts until 2019 to members of Gatland's backroom staff, including Howley and McBryde.
"The demand for the very best coaches is greater than it has ever been," added Phillips.
"When you have got a good coaching team it tends to work in World Cup cycles so what you don't want is a major disruption halfway through.
"Four years will become the norm. Warren picks his coaching team and his belief was this was the best team. We looked at everything."
Watch the Martyn Phillips interview on Scrum V, Sunday, 8 January, BBC Two Wales from 17:30 GMT.
Welsh Rugby Union chief executive Martyn Phillips expects Warren Gatland to return to his Wales role after coaching the 2017 British and Irish Lions in New Zealand.