The 19-year-old marked his first league start for the club with a fine long range strike against Southport at the weekend, as Town triumphed 5-1.
Watkins, a Hatters fans who used to watch the side from the terraces, made his debut as a substitute in an FA Cup third round tie at Southampton in January 2010.
He also made six appearances last season, scoring twice in the 4-0 FA Trophy win over Uxbridge.
Manager Gary Brabin said: “Adam was our stand-out player pre-season and has continued that into the season with a terrific goal and performance against Southport.
“This club has a fantastic proven track record of developing and nuturing young talent and Adam is another off of our production line.
““I must congratulate Adam - he has deserved this and long may his development continue.”