Sherwood worked with the Dane during his time at the north London club, but Spurs fans aren't too happy with the transfer - leading one to even burn old shirts with Eriksen's name and number on them.
Eriksen has verbally agreed to join Manchester United this summer, having spent last season on a short-term deal at Brentford.
The 30-year-old will undergo a medical ahead of a move to the north west once all the necessary paperwork is completed, where he is set to play under Erik ten Hag.
And Eriksen's former Spurs boss couldn't speak more highly of the creative midfielder who he coached between 2013 and 2014, but believes Man United need more players like him to challenge for the Premier League title.
"He's the best professional I've ever managed," Sherwood told talkSPORT.
"He's one of the fittest boys you're ever going to see, what he does off the ball is underestimated, and he's fantastic on it.
"It's an absolute no-brainer [to sign him] on a free transfer."
He added: "I hope Bruno [Fernandes] looks at Christian Eriksen and says, 'You know what, this is how you play as a team member'.
"Christian Eriksen knows exactly what the manager wants, he takes it to the pitch, and he takes it to the rest of his teammates. He's an absolute dream to manage.
"But he can't do it on his own. Of course, he's not going to take them to challenge Liverpool and Man City on his own, but if they had a few more like them [they might]."
There was a rumour that Tottenham manager Antonio Conte may be interested in bringing him back to north London but a deal never materialised.
But, while Spurs fans burn old shirts - apparently unhappy with a move to Man United - the United faitfhul will be hoping he can set Old Trafford alight.