He was co-opted as a Foyle MLA last October, to replace the former DUP MLA and assembly Speaker Willie Hay, who resigned that month for health reasons.
Mr Devenney said he is leaving his post because he wants to "concentrate on a number of local issues" in Londonderry.
The DUP said it will appoint Mr Devenney's successor "in due course".
In a statement, Mr Devenney said: "I have been deeply honoured to serve as an Assembly Member for the Foyle constituency.
"I was delighted when the party asked me to replace William Hay as the party's Assembly Member for the area.
"However after five months in the assembly, I have decided to step down from this role as I want to be able to concentrate on a number of local issues in the city. This is best achieved by being based in Londonderry."
He said he would continue in his role as a councillor and would "play an active role" in the DUP.
DUP leader Peter Robinson paid tribute to Mr Devenney and thanked him for his service in the assembly.
"I have enjoyed working with him.  He has always put the interests of the people he represents to the fore," Mr Robinson said.
The Democratic Unionist Party MLA Maurice Devenney has announced he is stepping down from the Northern Ireland Assembly after five months in the job.