In 2003, he signed with Polish club Anwil Włocławek, where he spent one season before returning to Latvia, where he joined BK Ventspils.

During his tenure with Bilbao, Blūms developed a reputation as a fierce competitor who is deadly from three-point range and can play lock-down defense.

[2] After his experience in Basque Country, Jānis moved back to Lietuvos Rytas, which played Euroleague that season.

[6] On 28 July 2020, at the age of 38, he signed with Pallacanestro Reggiana of Lega Basket Serie A (LBA)[7] but, by mutual agreement with the team, resigned after eight games played after the start of the season.

He reported to training camp by mid-August, and his season ended in mid-June as his team Liga ACB finals.