Craddock scored 38 in 86 appearances during two seasons at Kenilworth Road after signing from Middlesbrough for £50,000.
He was then sold to Oxford United in 2010 for a similar fee where he went on to net 28 goals in 87 games, and was one of of 12 players released by Oxford earlier in May.
Craddock, 26, said: “It excites me that if we’re doing well we’re likely to be playing in front of 15,000-plus crowds.”
Pompey manager Guy Whittingham added: “If you want to be promoted from one league to another then you have to bring in goalscorers and that’s what we have got with Tom.
Jones could loan out Muskwe and Mendes Gomes as he admits certain players would have left regardless of cup exit
Jones still keen on pushing for defensive signing ahead of deadline day
Former Aston Villa and Crystal Palace youngster Williams elated to make his full Hatters debut in Carabao Cup
Luton boss will make a late decision in the transfer window on whether to loan out Pereira
Jones hopeful that Onyedinma is soon over his 'unfortunate year' for Luton
“He’s a player that has a good ratio and we believe he will do well for us.
“I’ve watched Tom and he has a great work ethic. If he is not scoring goals he will keep going and be a right pest to defenders in League Two.”
Meanwhile, former Luton Town attacker Amari Morgan-Smith is one of a host of players who have been released by Conference rivals Macclesfield Town after joining them in the summer.
The 24-year-old, who netted 18 times in 48 for Town, only scored four league goals for the Silkmen last season and once during a loan spell with Kidderminster Harriers.
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