Damian Yeo Shen Li was born into a Peranakan family in Malacca, Malaysia on 31 March 1975.
In the 2013 Malaysian general election, Damian Yeo Shen Li was nominated by DAP to contest for the Alor Gajah federal seat.
In the 2018 Malacca state election, Damian Yeo Shen Li was nominated by DAP again to contest for the Duyong seat and won the seat and was elected to the Malacca State Legislative Assembly as the Duyong MLA for the first term after defeating Lee Kiat Lee of BN, Kamarudin Sidek of PAS and independent candidate Lim Jak Wong by a majority of 2,895 votes.
In the 2021 Malacca state election, Damian Yeo Shen Li was defeated by Mohd Noor Helmy Abdul Halem of BN by a slim majority of 200 votes.
Damian Yeo Shen Li announced his resignation as State Chairman of the DAP of Malacca, citing work commitments.