The pair were joined on the night by fellow legends and HOF inductees Bobby Smith and Martin Chivers as four of the club's greatest strikers - covering each era from the 1960s, 70s, 80s and 90s - all returned to the Lane.
Both saw it as a fantastic honour to join the club's greats on the Hall Of Fame, which is situated in the tunnel at the stadium.
Teddy, 124 goals in 277 appearances over two spells, said: "I am very honoured, especially when you look at the things some of those players won during their time here. There are players in the Hall of Fame that I looked up to such as Ossie Ardiles, Ricky Villa and Glenn Hoddle. When you see what they won and how they played the game in their era, it’s a real honour to be joining Spurs greats like that."
Clive, who memorably bagged 49 goals in all competitions in the 1986-87 season as part of his 84-goal haul in 135 appearances, added: "It is absolutely fantastic. When you set about playing football as a kid, you dream about playing for a big football club and if you can play for the team you supported, it is a wonderful feeling. The players already in the Hall of Fame are quite rightly the legends of this football club and I feel very proud and privileged to be named among them."
Teddy Sheringham and Clive Allen were inducted into our Hall of Fame in a special celebration at White Hart Lane on Thursday night.