The Portuguese head coach secured a return to Premier League management last week after Mourinho was appointed as Mauricio Pochettino’s replacement.
Mourinho took over the reins of the north London side nearly 11 months after Manchester United sacked the two-time Champions League winner.
His appointment at Spurs is controversial given Mourinho’s association with their bitter London rivals Chelsea FC.
Lampard won two Premier League titles, the FA Cup and the League Cup under Mourinho’s management.
The retired England international is currently in charge of Chelsea FC following his appointment in the summer.
Speaking at his pre-match media conference ahead of Chelsea FC’s trip to Manchester City on Saturday evening, Lampard backed Mourinho’s record as a manager.
“We had a couple of messages,” Lampard said. “I think history and results speak for themselves. He has done that consistently. It’s what we measure him and us as managers.
“He has got a good team. They were a lot of people’s favourites to be in the race. Pochettino did a great job.
“They have the structure there and will be a threat. They are in the top four race.
“When you look at the quality. The strength that they have, Kane and players like that.”
Chelsea FC started the weekend in fourth place and 12 points ahead of Mourinho’s Tottenham side in the race to secure a top-four finish in the Premier League this season.
The Blues turned to Lampard in the summer after Maurizio Sarri stood down as Chelsea FC manager to take charge of Serie A champions Juventus after just 12 months in charge.
Lampard’s previous managerial experience was limited to 12 months in charge of Derby County.
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