The U.S. insurer is exiting some Asian markets and in April sold South Korean unit to KB Financial Group Inc for $1.89 billion.
Taishin said its deal will require regulatory approval.
Prudential's Taiwan unit held assets worth T$165.55 billion in 2018 and has operated in the market for nearly 30 years.
($1 = 29.3740 Taiwan dollars)
(Reporting by Ben Blanchard and Emily Chan; editing by Jason Neely)