Former Chelsea striker Werner arrived on loan from RB Leipzig and 21-year-old defender Dragusin was signed on a six-year contract from Serie A side Genoa.
Tottenham will move into the top four if they win at Old Trafford and complete their first league double over United for 25 years, but are still contending with a long injury list.
Defender Ben Davies and midfielder Giovani Lo Celso are the latest players to be ruled out and although centre back Micky van de Ven is available again and Cristian Romero has returned to training, manager Ange Postecoglou is likely to blood his new recruits at United.
The fact that both Werner and Dragusin have been signed in the first half of January marks a change of tack for Tottenham who are renowned for leaving their transfer business late.
"We've been working on the centre back position pretty much since the summer window closed and there's been a whole list of players we worked through methodically," Postecoglou told reporters on Friday.
"A lot of that work has been done by the scouting department and (technical director) Johan (Lange) and (chief scout) Rob Mackenzie and the team started working into further detail.
"Radu was always on the radar as one of the players we thought would be a good option for us.
"I like his defensive attributes, his physical attributes, I think there's still a lot of growth in him."
With captain and leading scorer Son Heung-min on international duty with South Korea, Werner will give Postecoglou more striking options at Old Trafford.
The German had an underwhelming spell at Chelsea but Postecoglou is excited to have the German in his squad.
Asked if the striker has something to prove, Postecoglou said: "I don't look too much into that. When talking about bringing players in, for me it's do I see them playing in the team I've got right now and want to create.
"Obviously, Timo was at a point where he was looking for something to change and there was a possibility that moving was one of those options.
"He's still a good age, he's very motivated, he's got national team aspirations."
Tottenham are firmly in touch with the top four despite dealing with several long-term injuries to key players and suspensions.
"We have gone through a tough time and we're in an OK position," Postecoglou said. "We are not too far from where we want to be and the key for us is progress. The key to us is improving our football and hopefully we get some personnel back, which allows us to finish the season stronger."
