The Rt Revd Philip North turned down the post following objections to his stance against ordaining women priests.
He said he had withdrawn for "personal reasons" but added the "attacks" against him were "extremely hard".
The archbishops said the incident had raised concerns within the Church.
When he stepped down, Mr North said: "It is clear that the level of feeling is such that my arrival would be counter-productive in terms of the mission of the Church in South Yorkshire and that my leadership would not be acceptable to many."
In a joint letter, the Archbishop of Canterbury Justin Welby and the Archbishop of York Dr John Sentamu, said the events surrounding the appointment raised questions about the Church's 2014 commitment to the consecration of women bishops.
They said: "The recent events surrounding the nomination of Bishop Philip North as Bishop of Sheffield, including his withdrawal from the process, have understandably raised great concern amongst many in the Church of England.
"The status of the House of Bishops' Declaration, of June 2014 has been questioned by some and its meaning has also been challenged.
"We have therefore written to Sir Philip Mawer, the Independent Reviewer under the Declaration on the Ministry of Bishops and Priests, (Resolution of Disputes Procedure Regulations) 2014, to address the concerns that have arisen in the Church following these recent events."
It asks Sir Philip to examine five areas, including what efforts have been made to educate clergy and the public about the declaration and whether the nomination of Mr North was consistent with its terms.
The archbishops also used the letter to call on all those in the Church to "pray for those with whom they disagree, demonstrate mutual love and overcome those those things which in ourselves we find so divisive".

Boudicca Scherazade, 47, allegedly became obsessed with Laurence Roche after spotting him on his furniture stall in Wimbledon, London.
She sent photos of underwear and messages saying she was in love with him, and followed him around markets, it was claimed.
Ms Scherazade denies stalking.
St Albans magistrates were told how Ms Scherazade, from Middlesex, obtained Mr Roche's contact details from business cards left on his stall.
Her stalking campaign started after she gave him a bunch of flowers in 2013 and it continued until May 2016, it was said.
Prosecutor Clinton Hadgill read samples of the messages allegedly sent.
One included a photo of a pair of knickers on a rug with the caption "I've taken them off just for you".
In other messages, she is said to have told him: "I need your love so bad, can't live without you..."
It was claimed Ms Scherazade followed Mr Roche, who had a partner and child, to various markets and car boot sales, "continually" walked past his stalls, took photos of him and "caused him embarrassment" by shouting at him.
In the TV series Storage Hunters, Ms Scherazade, of Garrick Villa, Hampton, travelled the country with other dealers hoping to find a bargain. She appeared in the show in 2015.
She pleaded not guilty to a charge of stalking without fear, alarm or distress.
The case continues.

Tunnicliffe, 24, worked with Wigan boss Warren Joyce when he was coming through the Manchester United youth system.
Browne, 19, made his professional debut in the Europa League this season and has also played in the EFL Trophy.
"Marcus is a young player with great potential and will strengthen our group," said manager Joyce.
"Ryan has got a terrific attitude first and foremost. He has built up considerable experience now in this division and we are confident he can be a really positive influence to the group in the immediate future."
Both players are available for Wigan's Championship game against Brentford on Saturday.
Find all the latest football transfers on our dedicated page or visit our Premier League tracker here.

Alistair Roy missed a good chance to give the hosts the lead early on, pulling his shot wide.
Jonathan Page tested Shire's Richard Barnard with a close-range header and nodded another effort over.
Kinnaird fired in what proved to be the winner after increased pressure from the home side in the second half.
The Archbishops of Canterbury and York have called for an independent inquiry into the circumstances surrounding the failed appointment of a new Bishop of Sheffield.
[NEXT_CONCEPT]
One of the stars of reality TV series Storage Hunters stalked a market trader for three years and bombarded him with explicit messages, a court heard.
[NEXT_CONCEPT]
Wigan Athletic have signed midfielders Ryan Tunnicliffe and Marcus Browne from Fulham and West Ham on loan until the end of the season.
[NEXT_CONCEPT]
Lloyd Kinnaird's second-half strike helped East Stirlingshire defeat East Fife on the opening day of the Scottish League Two season.