Keene began his career at Fratton Park, but struggled for first team outings as he spent a much of his time out on loan.
He eventually moved on in 2007 and has spent the last six years turning out in Scandinavia.
The opportunity to head home has proven to be too good to turn down, with Keene delighted to be back in familiar surroundings.
Portsmouth's financial struggles mean he has only been offered a one-month deal, but that agreement could be extended if things go well.
Keene told Expressen: "It's no secret that it is a dream to play in the English league again.
"The club cannot afford to sign a longer contract. Portsmouth might look to loan me a month at a time."