HITC Sport understands the Belgian midfielder will join on loan.
The 21-year-old is a product of the Belgium club's youth system, making his debut back in 2013, and has since played over 60 games for the club.
He has started seven games for Standard this season but they have now agreed for him to join Boro, which will be on an initial loan until the end of the season with a view to a three-year permanent deal.
De Sart comes from a footballing family as his dad Jean-Francois used to play for them and was a former director of sport and his brother Alexis was also a product of Standard's youth system and only left last summer.
Boro moved for De Sart as they need cover in defensive midfield after losing Jack Stephens and Bruno Zuculini, who were recalled from loan spells by Southampton and Manchester City respectively.
Boro had a deal agreed with Benfica for defender Victor Lindelof earlier this month but that has hit issues and may not now be completed by Monday.