Elliott was not drafted by an Ontario Hockey League (OHL) team in 2001 and returned to York-Simcoe for Major Midget the following season.

For his efforts, he was selected as a finalist for the 2005–06 Hobey Baker Memorial Award,[1] collecting eight shutouts in 33 appearances, and leading the Badgers to the 2006 NCAA National Championship.

Elliott was invited to the Ottawa Senators' 2007–08 training camp, but was ultimately assigned to Binghamton on September 25, 2007.

He was recalled to Ottawa four days later to back up Martin Gerber, as starting goaltender Ray Emery was recovering from wrist surgery.

"[3] Elliott would finish the season in Ottawa, sharing goaltending duties with veteran Alex Auld.

Elliott's emergence effectively made Martin Gerber expendable to the team, and he would later be claimed on waivers by the Toronto Maple Leafs.

Elliott was nominated for the NHL's Rookie of the Month award for March 2009, though he would lose out to St. Louis Blues forward T. J.

[5] After winning just two of his 12 starts with the Avalanche, combined with a sub-par 3.83 GAA, Elliott was released as a free agent after Colorado declined his qualifying offer.

[7] Forming a formidable goaltending tandem with Jaroslav Halák, Elliott revitalized his career, posting a 23–10–4 record while sporting a 1.56 GAA.

After taking over for the injured Halák during the first round of the 2012 Stanley Cup playoffs, Elliott led the Blues to a series victory over the San Jose Sharks before ultimately being swept in round two by the eventual Stanley Cup champions, the Los Angeles Kings.

A 23–8–6 record during the 2015–16 NHL season earned Elliott the starting role for the Blues for the 2016 Stanley Cup playoffs.

He led the Blues to a first round victory over the defending Stanley Cup champion Chicago Blackhawks.

Elliott and the Blues would then move on to face the Western Conference's top overall team, the Dallas Stars.

Elliott's only faltering occurred in Game 6 of the series, when he was pulled in favor of Jake Allen after allowing three goals on seven shots.

He rebounded the next game, making 31 saves in a decisive 6–1 victory that propelled St. Louis to the Western Conference Finals for the first time since 2001 where they lost to the San Jose Sharks.

After spending the 2023–24 season unsigned, Elliott returned to the St. Louis Blues as a goaltending scout and development coach on June 17, 2024, marking the end of his playing career.