Sherwood was given the job on a permanent basis on Monday after taking over last week in a caretaker capacity from Portuguese Andre Villas-Boas who was sacked after an embarrassing 5-0 home drubbing by Liverpool.
"It's an honour to be head coach of this top club," the former England international told the Spurs website (www.tottenhamhotspur.com).
"I've known it from the grass-roots right up to the first team, worked at every level of the football club and played here, so I know it better than most. Hopefully that will stand me in good stead taking this club forward."
Spurs, who are seventh in the Premier League, decided on Monday to promote the inexperienced Sherwood from his role as youth development manager.
A highly-rated coach, the 44-year-old won the league as captain of Blackburn Rovers in 1995 before joining Spurs four years later.
Sherwood stayed at White Hart Lane until 2003, making almost 100 appearances for the club, before returning five years later to join the coaching staff.
His first game as caretaker coach was a 2-1 Capital One Cup quarter-final defeat by West Ham United last week but Spurs bounced back by winning 3-2 in the league at Southampton on Sunday.
"If you cut me in half I bleed the colour of the club," said Sherwood on Tuesday.
Spurs, who are six points behind league leaders Liverpool, entertain West Bromwich Albion on Thursday.