The 21-year-old spent last season on loan at Bristol Rovers and will re-join the club on a one-month loan on Monday.
The Denmark Under-21 international is highly-rated and Reading director of football Nick Hammond is delighted that the goalkeeper has signed a new deal.
“I am delighted Mikkel has signed, he is a top young goalkeeper and one of an excellent stable of keepers we have here,” Hammond told the club’s official website.
“He did very well last season, learning his trade and winning awards at a good club. He also drew a lot of praise after the Toulon tournament in the summer and rightly so, he is a young keeper on the right path and part of a very good group under Sal Bibbo’s coaching.
“[Rovers manager] Paul Trollope knows all about Mikkel and helped him develop last season, so we were happy for him to go back there for a month.
“He will get games under his belt, I know Rovers have good young keepers of their own but Mikkel has played nearly 40 games for them already, so this works well for us, Rovers and of course Mikkel himself.”
Andersen added: “It’s nice to get it sorted and I’m really looking forward to the three years, I’m really excited about my future.
“I want to stay at Reading and I want to prove myself here, so this is a great opportunity for me to do that.”
