Cardiff Blues flyhalf Anscombe only moved to Wales earlier this season and has made just nine appearances for the regional side.
Anscombe, 23, qualifies to play for his adopted country through a Welsh-born mother.
He is one of an uncapped quartet that also includes Newport Gwent Dragons centre Tyler Morgan, Scarlets prop Rob Evans and Blues hooker Kristian Dacey.
The omission of talented flyhalf Hook, now with English Premiership side Gloucester was no surprise given he has rarely won favour with Kiwi coach Gatland and was left out of the squad for the November internationals.
However, a recall had been forecast by some pundits for Adam Jones given Scarlets forward Rhodri Jones's shoulder injury.
But with Gatland selecting three tighthead props in Samson Lee, Aaron
Jarvis and Scott Andrews, there are now doubts over the extent of Adam
Jones's future as an international front-row forward.
Anscombe, in common with Hook, can play at both flyhalf and fullback although it remains to be seen if he will feature in Wales' matchday 23 for their Six Nations opener against England in Cardiff on February 6.
Rhys Webb, Mike Phillips and the fit-again Gareth Davies are Wales's scrum-halves.
"It's great to be able to name such an experienced squad that also boasts some exciting young talent," Gatland said.
"The four uncapped players have all been going well for their respective regions, and it will be good to see them in this environment and we hope they take the opportunity.
"They come into a squad packed with experience, and that experience will be important to us over the next eight weeks and the year as a whole," added Gatland, whose side defeated South Africa in November but lost to world champions New Zealand and Australia.
"We all know how tough the Six Nations is, and we kick the tournament off with a huge game against England, and that is something you have to be excited about and look forward to," added Gatland, whose side will also face England in their World Cup pool later this year.
Wales' 2015 Six Nations squad:
Forwards
Gethin Jenkins (Cardiff Blues), Paul James (Bath), Rob Evans (Scarlets), Aaron Jarvis (Ospreys), Samson Lee (Scarlets), Scott Andrews (Cardiff Blues), Richard Hibbard (Gloucester), Kristian Dacey (Cardiff Blues), Scott Baldwin (Ospreys), Alun Wyn Jones (Ospreys), Jake Ball (Scarlets), Bradley Davies (Wasps), Luke Charteris (Racing Metro), Dan Lydiate (Ospreys), James King (Ospreys), Sam Warburton (Cardiff Blues, Capt), Justin Tipuric (Ospreys), Taulupe Faletau (Newport Gwent Dragons)
Backs
Mike Phillips (Racing Metro), Rhys Webb (Ospreys), Gareth Davies (Scarlets), Dan Biggar (Ospreys), Rhys Priestland (Scarlets), Gareth Anscombe (Cardiff Blues), Cory Allen (Cardiff Blues), Jamie Roberts (Racing Metro), Jonathan Davies (Clermont Auvergne), Scott Williams (Scarlets), Tyler Morgan (Newport Gwent Dragons), Hallam Amos (Newport Gwent Dragons), Alex Cuthbert (Cardiff Blues), George North (Northampton Saints), Liam Williams (Scarlets), Leigh Halfpenny (Toulon)
Wales' 2015 Six Nations fixtures:
February 6: v England, Millennium Stadium, Cardiff
February 15: v Scotland, Murrayfield, Edinburgh
February 28: v France, Stade de France, Paris
March 14: v Ireland, Millennium Stadium, Cardiff
March 21: v Italy, Olympic Stadium, Rome