"The intervention of Oman had paved the way for his release, I understand," Vijayan said in a Facebook post.
The priest, who is "very weak", is undergoing treatment in Oman. All help will be provided to enable him to reach Kerala, the chief minister said.
Former chief minister Oommen Chandy said Keralites had been waiting to hear the news of his release for the last 18 months.
Father Uzhunnalil was abducted in March by Islamic State from port city of Aden after the terror group attacked a care home run by Mother Teresa's Missionaries of Charity.
He hails from Bharananganam in Pala in Kottayam.
BJP state president Kummanam Rajasekharan said the release was the result of External Affairs Minister Sushma Swaraj's "earnest efforts".
All steps should be taken to bring the priest as early as possible to his home state of Kerala, he said in a statement.
"Warm welcome to Fr. Tom Uzhunnalil to Kerala. Happy to note that the sustained diplomatic efforts by India on its own and along with the Oman government have yielded results," he said in a statement.
The release of Father Uzhunnalil is also an example that India won't tolerate extremist practices at any cost, he said.
"We are thankful to the Government of Oman and Sushma Swaraj ji who is always unrelenting in her efforts to bring back every Indian home," the MP said.
Catholic Bishops Conference of India president and Major Archbishop of the Syro Malankara church Baselious Cardinal Cleemis Catholicos thanked all those who helped in the release of Father Uzhunnalil.
The Cardinal also thanked Pope Francis for the Vatican's efforts in ensuring the release of the Keralite priest.
Cleemis also had a word of praise for the media for "keeping the issue alive".
Latin Catholic church head Archbishop Soosai Pakiyam also rejoiced the release of Father Uzhunnalil.
Thanksgiving prayers were also held in some churches as news of the release came in.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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