Having lost their opening game 37-14 to pre-tournament favourites New Zealand, Warburton's side have recovered magnificently to notch successive bonus point wins over Samoa (33-20) and Argentina.
Australia, who beat England 34-13, will now meet South Africa who were 33-5 victors over Ireland, while Wales will face New Zealand, who beat France 30-11.
Wales last reached the final in 1999 when the tournament was held in Wales, and have yet to win the World title at this age group.
Wales have made two changes for this match after Friday's 29-0 victory over Argentina. Llantrisant and Blues prop Patrick Palmer has had to return home with ankle ligament damage and has been replaced in the squad by Pontypridd's Sam Hobbs who will take up a place on the bench tomorrow.
The other change sees scrum half Gareth Williams in the starting line-up in place of Bridgend's Rhys Webb.
Head coach Justin Burnell said, "We came here with the aim of achieving a top four finish. We can be pleased that we have done that - and be excited about our next two games in the championship.
"If we are to improve and move forward as a nation, we have to get out of our comfort zone and play regularly against the best sides in the world - the southern hemisphere sides. We have already played New Zealand, Samoa and Argentina in Pool matches, now we have New Zealand again - then either Australia or South Africa on Saturday, either in the final or the third/ fourth place play-off.
"I am thrilled for this group of players and management. They are an extremely honest bunch and they are unsung heroes of Welsh rugby in a way. For many of them, this is the first taste of international rugby and they have all worked hard and just got on with whatever has been put in front of them."
IRB Under 19 World Championships Semi-final
Tuesday April 17, Ravenhill, kick-off 7.30pm (available to television viewers on BBC2 interactive via the red button or BBC Northern Ireland digital channel)
Wales Under 19 team v New Zealand (Tuesday April 17, 7.30pm, Ravenhill, Belfast)
Daniel Evans (Llanelli / Scarlets); Jimmy Norris (Bedwas / Dragons), Luke Ford (Wanderers / Blues), Rhys Williams (UWIC/ Scarlets), Leigh Halfpenny (Neath / Ospreys); Gareth Owen (Maesteg / Ospreys), Gareth Williams (Wanderers / Blues); Ryan Bevington (Bridgend / Ospreys), Huw Dowden (Beddau / Blues), Lloyd Elliott (Ospreys), Haydn Pugh (Llangennech / Scarlets), Josh Turnbull (Llanelli / Scarlets), Jevon Groves (Cardiff /Blues), Nicholas Cudd (Tumble / Scarlets), Sam Warburton (capt, Wanderers / Blues).
Replacements (from): Ben Roberts (Ebbw Vale / Dragons), Sam Hobbs (Pontypridd /Blues), Phillip Price (Bridgend Athletic / Ospreys), Nathan White (Bridgend / Ospreys), Lloyd Phillips (Narberth / Scarlets), Jonathan Griffiths (Glynneath / Ospreys), Rhys Webb (Bridgend / Ospreys), David Langdon (Ebbw Vale / Dragons), Tom Williams (Bridgend / Ospreys), Nicholas Harwood (Bonymaen / Ospreys), James Egan (Cardiff / Blues)