The Hatters - currently bottom of League One - have agreed to sell the player for £50,000. A further £25,000 will be paid depending on how many games he plays for the Tigers.
The 5'11" forward passed a medical at the KC Stadium today and has signed until 2007.
Sheffield-born Beckett - who will be 28 years old later this month - began his career as a Barnsley trainee before joining Chester City on a free transfer in 1998. He scored 25 goals in 70 league starts in a two-year spell before joining Chesterfield for £75,000. That move became the centre of an FA investigation of financial irregularities at Saltergate in 2001 which saw the club fined £20,000 and deducted 9 points, although they still just pipped the Tigers to an automatic promotion place that season.
After scoring 22 league goals in 58 starts, he left the Spireites to join Stockport for £100,000. He scored 45 goals in almost three years there, and played alongside current City strikers Ben Burgess and Aaron Wilbraham during their time at Edgeley Park, as well as Damien Delaney. The club couldn't meet the demands of their 7-goal top scorer over a new contract, so decided to cash in rather than lose him when his deal ran out at the end of the season.
The futures of players like Wilbraham are up in the air following Beckett's move. He's currently out on loan to Oldham, where he's scored 2 goals in 3 games, after failing to impress since a £100,000 move from Stockport to City in the summer. Danny Allsopp and Jon Walters may also find their places in Peter Taylor's plans threatened by Beckett's arrival.
He's expected to make his debut in the FA Cup First Round tie against Morecambe on Saturday alongside Nick Barmby. Delroy Facey should be fit to come back into contention as well following a hamstring injury.