Huth has joined Boro for a fee of £6m and has signed a five year contract. It was believed he would initially sign on loan but he has passed a new medical and has signed a permanent deal.
The ex-Chelsea player is still a couple of weeks away from full fitness so it is unlikely that he will be available for the game at Arsenal a week on Saturday.
Woodgate will be available to play at Arsenal after signing a loan deal for one year. The deal includes an option to buy the Boro-born defender at the end of the season.
There is no confirmation that Boro have signed Jason Euell as reported on Sky this afternoon.