The Welshman, who has held positions at Liverpool, Chelsea and Wrexham, links up with Gus Poyet at the Stadium of Light as the club completes a backroom clear-out
Angeloni and the club parted company on Wednesday in what represents a final clear-out of the club's staff under former coach Paolo Di Canio.
Angeloni was appointed in June last year along with former director of football Roberto De Fanti, following the departure of Bryan Robson, with Congerton taking up his post having previously been technical director at Bundesliga side Hamburg.
Congerton, who has also held back-room positions at Wrexham, Liverpool and Chelsea, will be tasked with overseeing player recruitment as well as the club's domestic and international scouting operation.
"I'm delighted to join Sunderland AFC and would like to thank the board and owner for this great opportunity," Congerton told the club's official website.
"Working alongside [coach] Gus [Poyet] and his team was one of the influential factors in me joining the club and something that I am very much looking forward to."
Poyet himself was happy with the appointment, with reports of a fractious relationship between the Uruguayan and De Fanti having preceded the Italian's departure.
"I would like to welcome Lee to the club," Poyet added.
"Recruitment is one of the most important areas in football nowadays, so I’m looking forward to working alongside Lee for the best of the club."