Estonian international Zenjov signed a one-year deal at Bloomfield Road after joining from Ukrainian side FC Karpaty Lviv.
And the 25-year-old aspires to become a favourite with the club's supporters.
He told the club's official website: "I am very happy to sign for Blackpool. It is a club with a long history and I'm looking forward to making a name for myself.
"The stadium is very nice and I have heard a lot about the fans. The team has supportive fans and I hope to be a fans' favourite."
He added: "I have played the majority of my career in the Ukrainian league, which is a quite competitive and tough league. I was there six seasons so I am experienced enough to come here and fight for a place in the team and help Blackpool. The coach knows my qualities and will use them in the right way."