The 25-year-old, who finished last season on loan at Northampton, has agreed a three-year deal with the Reds.
Collins is Crawley's 12th signing of the summer transfer window.
"James wants a new challenge and he comes with a very good goalscoring record in League Two," Reds boss Dermot Drummy told the club website.
Collins, who has previously had spells at Aston Villa, Swindon and Hibernian, scored 15 goals in 49 appearances last season.
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Some 853,000 16- to 24-year-olds were NEET at the end of 2015, down 110,000 on the same quarter of 2014.
But the figures also show the numbers were 5,000 higher than in the summer.
City and Guilds managing director Kirstie Donnelly said it was "worrying" to see the figures "creep up after months of more positive news".
The Office of National Statistics figures date back to October to December 2001 when 833,000 young people were classified as NEET, some 12.9% of the total age-group.
At the end of last year that proportion had fallen to 11.8%.
NEET numbers reached from highs of over a million, or more than 16% of the age-group, in 2011, but have fallen consistently since.
In England, the government raised the education participation age to 17 in September 2013 and to 18 in September 2015.
So young people in England are now expected to stay in full-time education, in an apprenticeship, or in employment with training until they are 18.
The UK-wide NEET figures first dropped below the million mark, to 987,000, or 13.5% of the age group in the first quarter of 2014.
England-only figures show there were 690,000 NEETs at the end of last year, almost 100,000 fewer than in the last quarter of 2014.
This figure is the lowest since 2000 when comparable records began and the number stood at 629,000, says the government.
Skills Minister Nick Boles said the figures showed the government was delivering on its commitment to ensure all young people were either earning or learning.
"There is no room for complacency, though, and through our plans to deliver three million new apprenticeships by 2020 and our qualification reforms, we are determined to build on these excellent results," said Mr Boles.
But campaigners say the figures are still too high
"More than one in every 10 teenagers is currently locked out of a path to the future," said Ms Donnelly.
And Jenny North, policy and strategy director of Impetus PEF, which funds projects to help the most disadvantaged young people, called for more government action.
"We need to see a clear focus from government on how they will help disadvantaged young people succeed in education, and progress into sustained employment so they can fulfil their potential," said Ms North.

28 August 2016 Last updated at 12:38 BST
Christopher Oates, who runs camel treks at Rosuick Farm on the Lizard Peninsula, said they were very sociable animals and would make great pets.
He said a successful breeding season meant the farm had more camels than required.
The camels, which range in age and trekking experience, are expected to sell for between Â£3,000 and Â£8,000.
League Two side Crawley Town have signed James Collins after the striker's contract at Shrewsbury Town was cancelled by mutual consent.
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The number of young people not in education, employment or training (NEET) is at its lowest for the time of year since 2001, UK-wide figures show.
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Up to 10 camels have been put up for sale at a farm in Cornwall.