Poom played as a goalkeeper for Lõvid, Sport Tallinn, KuPS, Flora, Wil, Portsmouth, Derby County, Sunderland, Arsenal, and Watford.

Poom made his international debut on 3 June 1992 in the Estonia national team's first official match since restoration of independence, a 1–1 draw against Slovenia in a friendly.

49 with a gold medal and enrolled at the Tallinn University of Technology, but didn't finish his studies, focusing on football.

On 26 March 1997, Poom joined Derby County for a reported transfer fee of £595,000, following a strong performance for Estonia (a 0–0 draw against Scotland, in a rearranged match played in Monaco).

[7] He made his Premier League debut on 5 April 1997, against Manchester United in Derby's 3–2 away win at Old Trafford, becoming the first player from Estonia to play in the PL.

Poom soon became a fan favourite, with supporters often confusing unfamiliar commentators with a low chant of 'Pooooom' before games, which sounded like booing.

Poom did not play nor did he make the substitutes' bench for the final, but was in Arsenal's 25-man European squad, each of whom won a silver medal.

[11] He made his debut for Arsenal on 8 November 2006 in a League Cup match against Everton, replacing the injured Manuel Almunia at half-time.

[16] Poom made his international debut for the Estonia national team on 3 June 1992, in a historic 1–1 friendly draw against Slovenia.