The suspected devices were found by a resident who reported the discovery to police.
A bomb squad from the Army were called to the scene in Greeno View Road, in the High Green area of the city, following the discovery on Friday afternoon (May 22).
A statement from South Yorkshire Police said: "An army EOD team also attended and carried out a controlled explosion on two devices found by a resident. The cordon has now been lifted and emergency services have left the scene.
"Police and partner agencies would like to thank residents for their patience."