The rights have been bought in a deal with cable and satellite channel Living TV, which already screens 'Grey's Anatomy'.
Of the two, 'Grey's Anatomy' is set to be the most eagerly awaited by terrestrial viewers because the ABC show has been a ratings success in the US, where it is regularly one of the top five most-watched shows and is seen as a succesor to the long-running 'ER'.
'Criminal Minds' is currently screened in the US on CBS and stars Mandy Patinkin, who was in 'Chicago Hope'.
Vanessa Brookman, Five's deputy director of acquisitions, said: "I am delighted that we have been able to acquire two top-rating US shows. We have a reputation for the finest American drama and these two series will make great additions to the channel."
Philippe Maigret, senior vice-president of sales and portfolio development for Buena Vista International Television, which distributes the two shows, said: "We're excited to be working with Five and Living TV to bring these two hit, critically acclaimed series to their viewers and are sure that the UK success of these shows will echo their strong US success."
Other US drama imports on Five have included the 'CSI' franchise and 'House', which stars Hugh Laurie as a grumpy American doctor.
These latest acquisitions come just weeks after Five's director of acquisitions Jay Kandola quit after less than a year in the post to take the same role at ITV.
Kandola had previously worked in the same role at Channel 4, where her commissions included 'The Simpsons', 'Lost' and 'Desperate Housewives'.
Meanwhile, Five has also announced a sponsorship deal with Rolls-Royce to support its broadcast of the 2005 Royal Institution Christmas Lecture.
The science lectures are aimed at young people and will be shown as part of Five's Christmas schedule. The deal, which runs from December 26-30, covers the opening and closing credits as well as break bumpers on the five one-hour programmes.
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