That is according to former Chelsea and Manchester United manager Jose Mourinho.
Luiz joined Arsenal on transfer deadline day for a fee of £8million.
The centre-back has a packed trophy cabinet behind him from his time at Chelsea, including a Premier League, Champions League and two Europa League triumphs.
However Mourinho, having managed Luiz, admits there are times when he loses concentration during a match.
But he believes a change of clubs will focus the 32-year-old’s mind and reckons it will turn out to be a good move for him and Arsenal.
“David is a player [Unai Emery, his former Paris Saint-Germain manager] knows well,” Mourinho said on Sky Sports.
“He knows what David can give and what David cannot give.
“I think we all know the good qualities of David and where he can improve teams.
“And I think we all know, probably I know a little bit better because I’ve coached him, that sometimes he makes mistakes, but he makes these mistakes especially when his concentration levels are low.
“And when you change to a new club and you have something to prove, I think it’s a good move for him.
“At this moment of his career to get this opportunity of a late move and stay in the Premier League at the highest level, for David, it’s a fantastic move.’
Mourinho, meanwhile, has questioned Arsenal’s signing of midfielder Dani Ceballos on loan.
The Real Madrid man will spend this season with the Gunners.
“Ceballos, I think they have other Ceballos’ in the squad,” Mourinho said.
“He’s a good player but I think they have other Ceballos’.
“When I see [Henrikh] Mkhitaryan, [Mesut] Ozil, Ceballos, they can play in different positions on the pitch and very similar characteristics.”