The controversy erupted after Lalit Modi, the chief of the IPL, said stakes worth about $15m in the team had been given to Sunanda Pushkar, Thaoroor's alleged girlfriend.
Critics have said the stake was a reward for Tharoor's behind-the-scenes services in putting together the consortium that bought the Kochi team.
Tharoor, an author and a former UN official, has repeatedly denied any wrongdoing, stating he helped secure the franchise to boost cricket in the southern state of Kerala, his home state.
But with pressure mounting on Tharoor and Pushkar, Pushkar's lawyer said on Sunday she had decided to give up her allotted stakes.
The row sparked uproar in parliament last week and held up discussions on the budget.
Tharoor, who spent almost three decades with the UN before quitting in 2007, was elected an MP last year.
He joined the Congress party in 2008 and has made enemies within the party for being an outsider who was elevated so rapidly.