He won two gold medals at the 2016 Summer Paralympics held in Rio de Janeiro, Brazil: in the men's 100 metres T35 event and in the men's 200 metres T35 event.

He won the gold medal in the men's 100 metres T35 and men's 200 metres T35 events at the 2017 World Para Athletics Championships held in London, United Kingdom.

At the 2019 World Para Athletics Championships held in Dubai, United Arab Emirates, he set a new world-record time of 11.07s in the men's 100 metres T35 event and also a new world-record time of 23.04s in the men's 200 metres T35 event.

[4][5] After winning the silver medal at the 100 m T35 during the 2020 Tokyo Paralympics Tsvetov refused to take a joint photo with Russian bronze and gold medallist Artem Kalashian and Dmitrii Safronov due to strained Russia–Ukraine relations.

Ihor Tsvietov firmly claimed the gold medal in the 100-metre race among representatives of the T35 class at the Paralympic Games 2024 in Paris, shaving four hundredths of a second off the world record.