It comes as the Labour Party prepares for local elections in May 2023, with voters in Bassetlaw and all other Nottinghamshire districts to go to the polls to elect councillors on the seven district and borough authorities.
Coun Greaves says his resignation will allow the Labour Group time to “identify a new leader and crystallise its ambitions and priorities for the future”.
He is expected to formally hand over the Labour Group leadership at the full council meeting on September 22, once a new leader has been selected by members of the Bassetlaw Labour Party.
In a statement issued to the Local Democracy Reporting Service, Coun Greaves said: “It has been the greatest honour to have led Bassetlaw District Council and the Labour Group over the last 10 years and I am immensely proud of what has been achieved in our district during this time.
“In my time representing the Council I have been honoured to work with dedicated officers and committed councillors who all do their best for Bassetlaw.
“Collectively, we have implemented a proactive agenda that has focused on jobs, inward investment, innovation, modernisation and change.
“There is much to be proud of in this time. I would also like to personally thank officers and staff at the council who worked tirelessly during the pandemic to support residents and businesses during an unprecedented time.
“They ensured that we continued to provide essential services both during the lockdown periods and as life has returned to normal, and have met each challenge head-on.
“Bassetlaw is a district full of potential with a bright future and I wish the next leader every success on delivering positive change for our residents.”
In the statement, he praised the authority creating jobs and opportunities, a skills hub, its council housebuilding programme and support for rough sleepers and vulnerable residents.
He also praised the support offered to veterans and local veterans and work with the Royal British Legion, and welcomed the district having “some of the finest green open spaces in the country”.
Last month, Coun Greaves confirmed his intention to run to become Labour’s prospective parliamentary candidate in the coming general election where, if successful, he could have taken on current Conservative MP Brendan Clarke-Smith.
But in a separate statement on Monday, he confirmed he has withdrawn his application due to the need for “greater diversity in Parliament”.
“I am standing aside in the hope that the Labour Party chooses a shortlist that reflects under-represented groups in society and in Parliament,” he said.