The pair will join the likes of Richard Hannon, Richard Fahey and Mark Johnston, after being given one horse each to train by the well-established syndicate.
Lambourn handler Watson will take charge of unraced two-year-old filly Cape Hill Cotter, while Spencer has been given a yearling colt by Requinto who was purchased at this week's Tattersalls Ireland September Sale.
Tim Palin, spokesman for Middleham Park Racing, said: "We obviously noticed that Archie is a very talented, young, up-and-coming trainer and we have agreed to support him.
"For the time being we will probably just be sending him the one and build it from there. Hopefully it will be the start of something bigger and better.
"The reason we have hooked up with Richard is that we were the underbidders on Rajasinghe last year who has since won the Coventry Stakes.
"We followed the horse closely after it won on his debut and, as a result, we have followed Richard all summer and he looks a very shrewd operator.
"He has been with Charlie Hills and Michael Bell so he has learned with some of the best and we look forward to working with him."