Spurs head coach Jose Mourinho has been desperate to bolster his attacking options and provide cover for Harry Kane, the club's only out-and-out striker in the first-team squad.
Vinicius must be granted a work permit but the deal is expected to be completed by this weekend, safely ahead of Monday's transfer window deadline.
The 25-year-old, who has never been capped at senior international level for Brazil, joined Benfica from Napoli last summer and scored 24 goals in the 2019-20 campaign.
Mourinho underlined his concern at the lack of cover for Kane prior to Tuesday's Carabao Cup penalty shootout win over Chelsea, claiming that with Kane left on the bench for a breather, he "had nobody" to play as a conventional striker.
He has, however, been confident throughout the last few weeks that Spurs would eventually sign another striker and that faith appears now to have been vindicated with Vinicius finalising a move to north London.