The Brazil international put pen to paper on a three-year deal with the west London side after Chelsea agreed a £34m transfer fee with Ligue 1 champions Paris Saint-Germain.
Luiz spent three-and-a-half seasons at Stamford Bridge before former Blues manager Jose Mourinho sold the versatile defender to PSG in a £50m deal in the summer of 2014.
The South American has won successive Ligue 1 titles during his stay at Parc des Princes but has failed to help the French club win an elusive Champions League crown.
Former Chelsea striker Sutton believes Antonio Conte has heaped pressure on himself with the questionable re-signing of Luiz on transfer deadline day.
“I am not sure about David Luiz, Antonio Conte has not put a foot wrong so can we question his judgement? Where will he play?” Sutton told BBC Sport during their transfer deadline day coverage.
“He is a maverick type, I am not so sure about him defensively. Conte has put himself under pressure with this one.
“There are players out there who would be more consistent that Luiz, I would rather go for steady – it is a gamble. He is a talent, can Conte get the best out of him?”
Luiz won the Champions League, the Europa League and the FA Cup during his first spell at Stamford Bridge.
The Brazilian centre-half netted 12 times in 143 games in all competitions between 2011 and 2014 at the west London side.
The South American could make his second Chelsea debut at Swansea City on Sunday 11 September.
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