Allen, 25, who joins the Royals on what the club describe as a long-term deal, could make her debut against Arsenal in the Continental Cup on Saturday.
Her Blues debut also came against Arsenal in 2013 in what was an all-English Champions League semi-final.
Allen's arrival comes after Bonnie Harwood left Reading to join Millwall.

Knockaert, 25, is on the shortlist alongside Leeds forward Chris Wood and Newcastle striker Dwight Gayle.
His father died in November, but he has been in fine form to help them maintain their place in the top two.
"For what happened with my dad this season I know he would be very proud of me if I win," he told BBC Sussex.
"I hope I will win it and it would be a great comeback for me from what happened for me this season.
"I didn't expect this when it happened, I was expecting myself to be out for a long time, I mean mentally."
Knockaert missed only one game following his father's death, while a number of his teammates and manager Chris Hughton travelled to France to support him at the funeral.
"I can just thank the club so much and all my teammates and everything to have helped me like they did," he continued.
"I think if I'm here in this position to try to be player of the season in the Championship, it's because of them, I owe them everything.
"Obviously it was tough - I'm not going to lie, it was really tough.
"But I still thought every morning when I woke up, I was just thinking about my dad and thinking I just need to fight for him and that's maybe the reason I'm here."
Brighton are in action again on Tuesday with a home game against Birmingham City and victory would put them top of the table.

The 26-year-old Durham paceman fractured a bone in his ankle during a County Championship match against Surrey last month.
Wood had already been forced out of the current Bangladesh tour.
He is set to miss the five Tests against India, the first of which begins on 9 November, and the one-day series that follows in the new year.
England's national physiotherapy lead Ben Langley said the new injury is unrelated to the problems that required two operations last winter.
"It was only when we got him in for a second scan that we discovered he'd been playing on despite having fractured a bone," he said.
"There's no reason to think that when he's had this bone fragment removed, he won't be able to get back to bowling as well he has for Durham, England Lions and England in the second half of the 2016 summer."

Llanelli MP Nia Griffith said "everything" will be discussed in the wake of the loss of the English safe seat.
She failed to give Mr Corbyn her full support in a BBC Radio Cymru interview.
Mr Corbyn has said he will not step down in the wake of the loss to the Conservatives.
Copeland had been held by Labour for more than 80 years - the Tories' Trudy Harrison won with 13,748 votes to Labour's Gillian Throughton's 11,601.
Speaking on Post Cyntaf, Ms Griffith said: "The Conservatives are very strong at the moment so there'll be a lot of questions raised now within the party.
"What's important now is discussing the whole thing and what happened in Copeland. Why has it happened and what is the best way forward?"
Asked if the loss raised questions about Jeremy Corbyn's leadership, she said: "There will be a lot of discussion about every aspect of our party now and that will probably form a part of it".
When asked if she would resign to trigger another leadership ballot, she added it was important the party rebuilds and needs to be better prepared for future elections.
Meanwhile Gerald Jones, a Labour shadow Welsh minister, told BBC Radio Wales the result was "a significant set back for us as a party and one that we have to now rebuild from".
The Merthyr Tydfil MP said the Labour party has to "take stock" with a "lot of work to do".
Mr Corbyn said while it was "a day of disappointment in Copeland" he would not be quitting as Labour leader.
Asked if he would fall on his sword following the defeat, he said: "No. I was elected leader of this party - I'm proud to lead this party."
Reading have signed midfielder Remi Allen from Women's Super League One rivals Birmingham City for an undisclosed fee.
[NEXT_CONCEPT]
Brighton winger Anthony Knockaert says he wants to win the Championship Player of the Year award for his family following the death of his father.
[NEXT_CONCEPT]
England bowler Mark Wood is to have a third ankle operation and is likely to miss the Test series in India.
[NEXT_CONCEPT]
Jeremy Corbyn's future will form part of discussions around the fall out of the Copeland by-election, Labour's shadow defence secretary has said.