EgyptiaMr Morsi and his Muslim Brotherhood movement hope the election will put an end to increasingly vocal opposition and street protests, analysts say.
The Islamist-dominated parliament was dissolved last June after judges ruled election laws were unconstitutional.
In the last elections, in January 2012, the Muslim Brotherhood's Freedom and Justice party won roughly 40% of the vote.
Egypt is deeply divided between Mr Morsi's Islamist supporters and a liberal-led opposition, and has been wracked by unrest, insecurity and an economic crisis.
Tensions have intensified since an Islamist-backed constitution - criticised for failing to protect key rights - was adopted in December.
Thursday's decree states voting will take place in:
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- Cairo and four other provinces on 27-28 April, with a run-off scheduled for 4-5 May
- Giza, Alexandria and six other provinces on 15-16 May, with a run-off scheduled for 22-23 May
- Eight provinces on 2-3 June, with a run-off scheduled for 9-10 June
- Six provinces on 19-20 June, with a run-off on 26-27 June
The new People's Assembly will be invited to convene on 6 July, the decree said.