It may have happened anyway, no matter who played the Tenth Doctor, but it was during Tennant's Tenure as Ten that we got two strong spin-offs from the original 'Doctor Who'.
Captain Jack Harkness was introduced during Christopher Eccleston's year-long portrayal of the Ninth Doctor, and Torchwood was mentioned during his penultimate episode, "Bad Wolf". But it was after Ten was piloting the TARDIS that we saw him spur the creation of the Torchwood Institute in 1879, and get caught in a three-way battle between the Daleks, the Cybermen, and Torchwood at Canary Wharf.
And Sarah Jane Smith never ran into any of the following incarnations of the Doctor after she was unceremoniously dumped as a Companion by the Fourth Doctor. (Her involvement in "The Five Doctors" took place while she was still the Companion to the Third Doctor.) She finally crossed paths with Ten in "School Reunion", and that seems to have led to the creation of 'The Sarah Jane Adventures'. That show is geared more towards the younger set while 'Torchwood' is for a more adult audience than that targeted by 'Doctor Who'.
So even though Tennant isn't technically responsible for this expansion of the TV Universe, it can't be argued that his participation helped propel these two characters to their own series.