As a full international between 1968 and 1980, he won 77 caps for the Sweden national team and represented his country at the 1970, 1974, and 1978 FIFA World Cups.

[1] During a brief period, Hellström trialed with local giants Malmö FF after getting invited by former national team player and then youth coach, Karl-Erik Palmér, but did not join the club on permanent basis.

On his own initiative, Hellström sought to continue playing football at Hammarby IF since he had read about the club's youth academy in a magazine.

[2][3] On 11 May 1966, aged 17, Hellström made his debut for Hammarby IF's senior team in a 3–1 away win against Avesta AIK in Division 2 Svealand, his only appearance throughout the season.

Although the team suffered a relegation, Hellström was voted as the best goalkeeper in the league by Sweden's dominating sports magazine Idrottsbladet.

Returning to Allsvenskan in 1970, the club was placed last in the table after eight rounds in July, but went practically unbeaten through the rest of the campaign, eventually finishing fifth.

In both 1972 and 1973, Hammarby finished mid-table in Allsvenskan, being unable to produce any sort of challenge for the Swedish champion title, but Hellström continuously stood out as the best goalkeeper in the league.

The club also competed at continental level, most notably reaching the semi-finals of the 1981–82 UEFA Cup, being eliminated by the tournament's eventual winners IFK Göteborg through 2–3 on aggregate.

Beloved by the Kaiserslautern fans for his performances and loyalty to the club, most notably turning down a lucrative offer from New York Cosmos, he became the first ever non-German player to be granted a testimonial match.

In 1988, Hellström made a brief comeback, playing one match in Allsvenskan for GIF Sundsvall, due to injuries at the club, aged 39 years, 7 months and 18 days.