The tour, which begins on September 30 and will include two Tests and three ODIs, had been called into question after an attack in July on a cafe in Dhaka in which 20 hostages were killed, including 18 foreigners.
Morgan had already spelled out the reasons for his personal concerns about travelling following his previous experience of security alerts in both India and Bangladesh.
And the ECB confirmed late Sunday that both Morgan, 30, and Hales, 27, had let England cricket chief Andrew Strauss know their decision this weekend.
“Whilst we understand and respect Eoin and Alex’s decision, we are disappointed that they have made themselves unavailable for selection for the Bangladesh tour,” Strauss said.
“We have had open and honest conversations with all the players about the security arrangements in Bangladesh and at this stage we are not expecting any other individuals to withdraw from the tour.
“Final selection for the Bangladesh tour, will now take place on Friday.”
Strauss added: “As with all England overseas tours, the safety and security of players and staff is of the utmost importance to ECB.
“We will continue to monitor the situation in Bangladesh, take advice and consider the appropriate steps up to and throughout the five weeks we are on tour.”
Lancashire wicketkeeper-batsman Jos Buttler will captain the one-day side in Morgan’s absence, the ECB said.
Buttler, the vice-captain, has led England only once before in a Twenty20 international against Pakistan last winter.
Following the July attacks the ECB sent an inspection team to Bangladesh led by their long-serving security chief Reg Dickason.
After he reported back, the board confirmed last month that the tour, which is scheduled to run until November 1, would go ahead as planned.
“A thorough and detailed risk assessment was approved and accepted by the ECB Board and the England players and management have been fully briefed on all aspects of the safety and security arrangements,” the ECB statement added.
Morgan explained last week his thinking had been influenced by a bomb exploding at a 2010 Indian Premier League match and the violent background to a brief spell in the 2013/14 Dhaka Premier Division.”In 2010 we played an IPL game in Bangalore and a bomb went off in the ground. We immediately left for the airport. So that was an instance. Another one was (in) Bangladesh playing domestic cricket during political elections when things were incredibly violent.”
The Irishman added: “I think ultimately, as I’ve said before, as an individual you need to be comfortable within yourself to focus on cricket.
“I’ve been to places before where things have become a distraction and it’s only been once or twice when security’s been a distraction and I’ve told myself I’d never put myself in that situation again.”
Test captain Alastair Cook is understood to have given a private assurance he will be on the tour, while coach Trevor Bayliss, who was on the Sri Lanka bus that came under armed attack in Lahore in 2009, has stated publicly he will travel to Bangladesh.