Sadanand Shet Tanavade filed his nomination papers at the Goa Assembly complex.
Vinay Tendulkar is currently member of the Upper House of Parliament from Goa and his term his expiring this month-end.
Sadanand Shet Tanavade filed his nomination papers before Returning Officer Namrata Ulman at the Goa Assembly complex in the presence of Chief Minister Pramod Sawant and other MLAs.
"I am thankful to BJP president JP Nadda, Prime Minister Narendra Modi, Union Home Minister Amit Shah, BJP general secretary BL Santhosh, Goa Chief Minister Dr Pramod Sawant and my party for giving me this opportunity," Mr Tanavade said after filling the form.
He claimed all MLAs of the BJP and supporting parties were present during filing of the nomination.
Mr Tanavade said he will request even the opposition MLAs to vote for him.
The BJP and its allies have 33 MLAs in the 40-member Goa Assembly. The opposition Congress has three MLAs, Aam Aadmi Party (AAP) has two members, and the Goa Forward Party and the Revolutionary Goans Party have one legislator each.
Meanwhile, AAP's Goa president Amit Palekar said his party will not field its candidate for the Rajya Sabha poll as it does not have the required numbers and it will also not participate in the election process.
"We don't want to waste the precious time of the Assembly. We don't appreciate that. We will contest the Rajya Sabha election whenever we have numbers in the Goa Assembly," Mr Palekar told reporters.
Asked about supporting the Congress candidate, Mr Palekar said the party is yet to announce its candidate for the election.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)