Following a successful trial, the 28-year-old has put pen-to-paper on a short-term deal at Ewood Park until the end of the 2015-16 season.
The move sees Jackson reunited with manager Paul Lambert after the pair enjoyed a successful spell together at Norwich City.
"It has been a good two weeks coming in and getting a feel for the club, so I'm delighted to finally put pen-to-paper now.
"Everyone has been very welcoming, it is a warm club and I'm just delighted to be here and be able to play a part of what the gaffer is doing here.
"I'm very hungry to do well. I've had a few ups and downs in the last few years, so I'm definitely looking forward to this opportunity.
"It is a great club, a great set of lads and a great manager. I think the timing has worked out well, so I'm really looking forward to it."
Born in Jamaica, Jackson moved to Canada as a child where he started out in youth football, before moving to the UK as a teenager.
After catching the eye at non-league level, the forward moved to Rushden and Diamonds at the age of 17 and his footballing career really took off with 42 goals in 93 appearances.
That prompted Gillingham to move for his services in 2008 and he continued his fine goalscoring form with another 42 goals in a two-year spell.
A big money move to Norwich City followed as boss Paul Lambert paid £600,000 to take the forward to Carrow Road in the summer of 2010 and it was his goal against Portsmouth in May 2011 that saw the Canaries clinch promotion to the Premier League.
With the departure of Lambert to Aston Villa, Jackson saw his game time with Norwich limited and he left for Bundesliga side Eintracht Braunschweig in July 2013.
He has since had spells with Millwall, Coventry City and Barnsley, before linking up wth Lambert once more at Ewood Park.