The DUP MLA has been receiving medical treatment since suffering heart problems last month.
In a letter read to the assembly, he said he would be stepping down as MLA for Foyle next Monday to concentrate on returning to good health.
Sinn FÃ©in's Mitchel McLaughlin took on the role of Speaker last month in a temporary capacity.
A DUP elected representative since 1981, Mr Hay played a key role in resolving parading tensions in Londonderry.
Mr Hay was elected Speaker in May 2007 following the restoration of devolution to Northern Ireland.
Before his illness, the Donegal-born politician had been due to leave the post after becoming a member of the House of Lords in August, deciding to sit on the crossbenches.
Last month, he suspended a member of his staff after the discovery of an irregularity in his office allowances.
Shortly afterwards, he became ill and has been absent from the assembly chamber since then.
First Minister Peter Robinson said Mr Hay's "qualities of hard work and devotion to his constituents have been reflected in election after election".
The DUP leader said that in Mr Hay's role as Speaker, his party colleague had shown "absolute impartiality and fairness".
"He always defended the rights of assembly members to full and fair participation in debates and at all times sought to ensure the tone of debate was measured and respectful: sometimes not an easy task in Stormont," he said.
The Northern Ireland Assembly Speaker William Hay is to retire next week.