The New Zealander is widely expected to be appointed on Wednesday.
Gatland led the Lions to a series win in Australia in 2013 and has been named as the leading contender for the job by Lions chief executive John Feehan.
"He's the outstanding candidate," former Wales and Lions flanker Williams told BBC Scrum V.
"He's been on the last two Lions tours, assistant in 2009 and head coach four years ago.
"You look at the other candidates and contenders and they wouldn't have been on another Lions tour, which is so valuable.
"It's going to be a tough ask, but I think it's definitely the right choice."
Ireland boss Joe Schmidt and England coach Eddie Jones had been touted as contenders for the job, but Jones ruled himself out of the running for the post earlier this year.
Gatland helped the Lions secure their first series win for 16 years in Australia and Welsh Rugby Union chief executive Martyn Phillips has said he would not stand in the 52-year-old's way if the Lions role is offered to him again.
The Lions have not won a series against New Zealand since 1971.
But former Wales fly-half Jonathan Davies thinks the Lions could run Steve Hansen's world champions close in 2017.
"New Zealand away is daunting, but I do feel that [with] the calibre of player in the northern hemisphere I've got a sneaky feeling that they might have an opportunity to shock the All Blacks," he said.
2017 British and Irish Lions tour fixtures:
3 June - Provincial union team (Toll Stadium, Whangarei)
7 June - Blues (Eden Park, Auckland)
10 June - Crusaders (AMI Stadium, Christchurch)
13 June - Highlanders (Forsyth Barr Stadium, Dunedin)
17 June - Maori (International Stadium, Rotorua)
20 June - Chiefs (Waikato Stadium, Hamilton)
24 June - New Zealand (First Test, Eden Park, Auckland)
27 June - Hurricanes (Westpac Stadium, Wellington)
1 July - New Zealand (Second Test, Westpac Stadium, Wellington)
8 July - New Zealand (Third Test, Eden Park, Auckland).
Wales coach Warren Gatland is the right man to lead the British and Irish Lions on their tour of New Zealand next summer, says Martyn Williams.