  Given bipartite graphs $H_1$, \dots , $H_k$, the bipartite Ramsey number
$br(H_1,\dots, H_k)$ is the minimum integer $N$ such that any $k$-edge-coloring
of complete bipartite graph $K_{N, N}$ contains a monochromatic $H_i$ in color
$i$ for $1\le i\le k$. There are considerable results on asymptotic values of
bipartite Ramsey numbers of cycles. For exact value, Zhang-Sun \cite{Zhangs}
determined $br(C_4, C_{2n})$, Zhang-Sun-Wu \cite{Zhangsw} determined $br(C_6,
C_{2n})$, and Gholami-Rowshan \cite{GR} determined $br(C_8, C_{2n})$. In this
paper, we solve all remaining cases and give the exact values of $br(C_{2n},
C_{2m})$ for all $n\ge m\ge 5$, this answers a question concerned by
Buci\'c-Letzter-Sudakov \cite{BLS}, Gholami-Rowshan \cite{GR}, Zhang-Sun
\cite{Zhangs}, and Zhang-Sun-Wu \cite{Zhangsw}.
