The pair, both 18, impressed manager John Still and the coaching staff in their final year of their scholarships last season.
Goalkeeper King has been on the Town’s academy books since he was an U12, while midfielder Galliford has been in the Hatters’ academy set-up for 10 years.
King was unused substitute 11 times for the first team last season in the absence of the injured Mark Tyler and played six times for the Town’s development squad.
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Luton-born Galliford was a regular for Paul Driver’s U18s last season, scoring 11 times and earned a number of call-ups to the development squad, scoring two marvellous goals in the last match against Gillingham.
Hatters boss John Still told the club’s official website: “Both players have shown a tremendous attitude and have worked really hard to get to this point.
“They don’t need me to tell them that the hard work starts now, but they are young, talented players who we will be watching closely over the next 12 months.
“In the last year they have shown us what they are capable of. In Craig’s case he’s done well out on loan at Bromley and the Met Police, while Isaac improved and improved over the course of the season, so much so he warranted the opportunity to become a pro.”