Moyes will be unveiled on Thursday afternoon as the new manager of the Basque outfit, seven months after being sacked by Manchester United following a dismal first season in charge.
The Scottish manager has agreed a one-and-a-half-year deal with the La Liga outfit.
Arteta, who played under Moyes for six years at Everton and also spent a season with Sociedad, said on www.marca.com: "I am aware that Moyes has reflected after what happened to him in Manchester and he will know what he has to change.
"A manager that succeeded 10 years at Everton, but whose 10-month stay at United didn't go to plan, does not forget how to coach.
"Moyes is on top of players so that they always give their best. If you do then he makes your week much easier."
Mikel Arteta on David Moyes
"I have spoken to him (Moyes) and I have told him that he is going to a marvellous place.
"He is going to find a club that in many aspects resembles Everton.
"It's like a family and with a group of players that are currently in a lower position that they deserve to be in."
Arteta played for Sociedad in the 2004-05 campaign before moving to Goodison Park and believes the club's players will enjoy working with Moyes.
"David has a lot of personality," the 32-year-old said. "His teams always have to take the initiative.
"He likes to maintain a very united group and he gives a lot of importance to it.
"Moyes is on top of players so that they always give their best. If you do then he makes your week much easier.
"Moreover, he also takes a personal interest in his players as well."
The 51-year-old Scot is looking to rebuild a reputation damaged by his disappointing spell at Old Trafford.
He succeeded Sir Alex Ferguson at United in the summer of 2013, but was shown the door just 10 months into a six-year contract with the Red Devils.
Moyes inherits a Real Sociedad side that sit 15th in La Liga.
Real Sociedad dismissed coach Jagoba Arrasate last week after a dismal start to the campaign.
The San Sebastian-based club - who finished fourth in 2013 and seventh last term - won just one of their opening 10 league fixtures.
Moyes' first game in charge will be the trip to newly-promoted Deportivo La Coruna on November 22.
The ex-Preston tactician becomes the fourth British manager of Real Sociedad, following in the footsteps of Englishman Harry Lowe and Welsh duo John Toshack and Chris Coleman.