She replaces Jo Stevens, who resigned last month in protest at an instruction that Labour MPs should back the bill to trigger Brexit.
Ms Rees is the fifth appointment to the role since the 2015 general election.
Mr Corbyn said his team's strength would "develop Labour's alternative plan to rebuild and transform Britain".
In other appointments, Rebecca Long-Bailey becomes shadow business secretary, Sue Hayman takes the environment, food and rural affairs brief, and the new shadow chief secretary to the Treasury is Peter Dowd.
Ms Rees was a shadow justice minister in January 2016 but resigned after the EU referendum, only to return to the job in October 2016.
She backed Andy Burnham for the Labour leadership in 2015 and Owen Smith in 2016.
A former Welsh squash international who won more than 100 caps, the new shadow Welsh secretary was preceded by Ms Stevens, Paul Flynn, Nia Griffith and Mr Smith.
Ms Rees was previously married to former Labour Welsh Secretary Ron Davies.
Christina Rees is the fourth MP to hold the shadow Welsh secretary's job under Jeremy Corbyn - and the fifth since the general election less than two years ago when she entered parliament.
She supported Owen Smith's challenge to Mr Corbyn's leadership last year but voted with the Labour leader to trigger Brexit this week.
Eight Welsh Labour MPs rebelled in that vote, including Shadow Arts Minister Kevin Brennan.
Unusually, the Cardiff West MP and other frontbench rebels are likely to keep their jobs, a sign of Mr Corbyn's limited authority as leader.
Labour leader Jeremy Corbyn has named Neath MP Christina Rees as the new shadow Welsh secretary.