Pochettino signed a five-year contract at White Hart Lane on Tuesday after resigning at Southampton.
The 42-year-old guided the Saints to an eighth-place finish in the Premier League table last season.
Following the Argentine's success at St Mary's Stadium during the 2013-14 campaign, Gross is confident that Pochettino is the right man to lead Spurs forward.
"First of all I'm sad for [former manager] Tim Sherwood because he has quite a good record when he managed Spurs last season, and I'm quite happy for Pochettino because he did extremely well with Southampton," he told Sky Sports News.
"I remember two years ago the former chairman at Southampton wanted to absolutely change the philosophy of coaching and training, so he put in Pochettino from Spain. And he made a big impact with this team.
"So I guess Pochettino has the capacity to repeat this performance, and to better because [Tottenham] want to finish in the top four."
Gross took charge of Spurs in 1997, but he was sacked just nine months into the job following a string of poor results.