Moyes was confirmed as the new head coach on Monday, replacing Jagoba Arrasate after the club slumped into the bottom three of the Spanish top flight.
Retired Dutch goalkeeper Westerveld, who had a short spell under Moyes at Everton, was with Sociedad for four seasons after leaving Liverpool in 2001 and believes the former Preston North End boss has picked the perfect club to relaunch his career.
"It's one of the clubs I feel most connected with so I am really happy with this move," the 40-year-old, currently coaching with Ajax Cape Town in South Africa, told Perform. "When I heard this news I felt this is the best news for Real Sociedad, as I saw they were talking to other coaches, but I think for the club this is a great move."
Moyes was sacked by Manchester United eight months after replacing Alex Ferguson at Old Trafford, and has waited over half a year make his return to football management.
But Westerveld believes Moyes' reputation remains intact, even after his chastening experience with United.
"I think David Moyes is a big name. He struggled at Manchester United, but he still has a good name as a coach," he added.
"What I've heard is that most of the people are happy with him, he's not a low-key coach from England, he is a quality one. The people will be happy with him.
"It's maybe a smart move for him. It's one of those clubs in Spain that is a very stable club, they don't have a president who throws money away and sacks coaches every couple of months.
"The club is famous for its scouting system and for developing younger players, so I think he should feel at home.
"It's a little bit like Everton, it's a decent club. When they have a good year they reach the Champions League, normally they play mid-table.
"It's a good, well-structured, decent club. He will feel at home. He won't have any pressure if they lose a couple of games, they have a lot of faith in their foreign coaches."
One concern that has been raised following Moyes' appointment is the language barrier, but Westerveld does not expect it to stop him settling into life in San Sebastian.
"I don't think there will be any problems," he added. "It depends who he brings with him, but when I was there we had a French coach there who couldn't speak a word [of Spanish].
"They just bring in translators."
Sociedad sprung a surprise on Atletico Madrid on Sunday, winning 2-1 under the caretaker charge of Asier Santana to move up to 15th in the table.
Moyes' first match will come after the international break when his new charges travel to Deportivo La Coruna on October 22.
