The 25-year-old German was on the losing side in last season's UEFA Champions League against Frankfurt.
Blues have also brought in a player from the winners Frankfurt, German international forward Isabelle Linden.
They also signed Norwegian midfielder Andrine Hegerberg this week from Swedish side Kopparbergs/Gothenburg
"To sign Paris Saint-Germain's number one goalkeeper says it all," said Blues Ladies manager David Parker. "We have had to work hard to prise her away.
"It is another signal of intent and statement that we can attract the very best players to the club with the vision and strategy we have.
"When meeting Ann-Katrin and showing her everything we had to offer at the club she was blown away by what we are developing here and wants to be part of this special journey we are embarking upon."
The arrival of Berger, Linden and Hegerberg comes on top of the signings of Corina Schroder from Liverpool and Marisa Ewers from Bayer Leverkusen.
But Blues have lost two players, England internationals Jade Moore and Jo Potter having both opted to leave, after buying out their contracts.
Blues stand third in Women's Super League One, seven points behind leaders Manchester City, having gone into the mid-season break with two wins in three matches.

The road bridge over the River Wharfe at Tadcaster, near York, partially collapsed in December.
Currently the river can only be crossed using a temporary footbridge.
North Yorkshire County Council said "persistent and unusually high river levels" had delayed the work, which had been expected to finish by next month.
In a statement, the authority said: "The County Council has learned in the last few days that the primary cause is damming of the river by Network Rail five miles downstream at Ulleskelf for work on a railway bridge.
"Although the Environment Agency issued a permit for this work to be carried out, North Yorkshire was not notified about the operation."
Councillor Chris Metcalfe said: "We are extremely frustrated by this development."
Network Rail said it had "agreed the terms of our work with the Environment Agency prior to accessing the river" and was first made aware of the issue on Wednesday.
"After speaking with the Environment Agency today, we have agreed to remove our worksite from the river to allow water levels to drop and essential work to take place at Tadcaster."
The Environment Agency said: "We regulate work in rivers to ensure that any works carried out do not increase flood risk. When we issue a permit we take into account flood modelling data and determine if consent can be granted under Environmental Permitting Regulations. Our decision does not take into account whether one project is more or less important than another, whether they are related to rail infrastructure, road infrastructure, or other purposes."
The government pledged £3m for repair work within days of the bridge collapse, and £1.4m was given by the region's Local Enterprise Partnership to widen and strengthen the bridge.

American Chris Zablocki again finished second, while James Faudemer was the first Jersey runner home in a new personal best of 2:39.15.
Nollaigh O'Neill, who led from early on, dominated the women's race.
"I'm so happy, but the time was slow," said the 44-year-old Irish runner.
"I was flying up until about mile 20 or 21 and my quads started to seize and tighten up, so I just had to pull back and run strong and smart."
O'Neill made it over the line at the Weighbridge just outside the three hour mark (3:01.48) and more than 10 minutes clear of second-placed Ffion Davies.
More than 400 runners took on the full 26-mile course, with hundreds more in the 3K fun run and relay events.
While Troshkin stole the headlines in the men's race, Faudemer's run smashing quarter of an hour off his personal best was amongst the local highlights.
"I'm just so happy," Faudemer told BBC Radio Jersey.
"Long distance running is picking up in Jersey - I knew I had it in me with the sessions I've done in the build up.
"The support was amazing throughout the whole course, friends and family, it was awesome and made a big difference."
SportsHub Men, featuring Jersey's top triathlete Dan Halksworth, took the relay title while SportsHub Women were the first female team home.
Peter Holmes won the 3K race, narrowly ahead of Jack Kennedy.
Birmingham City Ladies have made their third foreign signing of the mid-season break by bringing in Paris St-Germain goalkeeper Ann-Katrin Berger.
[NEXT_CONCEPT]
The completion of repair work to a Grade II listed bridge damaged by winter flooding last year has been delayed until January.
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Russian Aleksey Troshkin won the Jersey Marathon for the third year in a row, with his time of two hours, 18 minutes and 28 seconds just outside his own course record.