Morgan led England to their maiden success in a 50-over World Cup in July, with the final settled in dramatic fashion at Lord's – the tournament hosts edging out New Zealand in a super over.
Following the tournament, the 33-year-old suggested he was undecided as to whether he should stay on as captain of the limited-overs side. (CRICKET NEWS)
However, the ECB confirmed on Friday that Morgan would remain in charge and Giles is delighted with the batsman's decision with England now having the T20 World Cup in their sights.
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"Eoin took some time to decide whether, all things considered, it was right to continue," Giles told Sky Sports.
"It didn't take him too long, thankfully. I'm delighted, he's been a great leader for us and with us losing [coach] Trevor Bayliss as well it's great for the team and the environment that he's staying on.
"Having one of those two guys still there gives us consistency and now we can look to perhaps go with the team we've got and to hold two white-ball trophies within a year would be a great achievement."
Bayliss called time on his tenure as England coach across all formats at the end of the Ashes series, but Giles is confident a replacement will be finalised within the coming weeks.
"I see one coach leading the whole thing. I've been part of a set-up where there are two coaches and role-playing that out, for me, it doesn't end particularly well," Giles told BBC Sport.
"If we have one head coach and some very good assistants, we are going to have to look after those guys well. The head coach would have some time off, so it's an opportunity for those assistants to lead in different forms.
"I hope we have a shortlist in a week to 10 days and we will go through interviews. We won't rush it but it would be nice to have someone in place before we leave for New Zealand."
Giles also added Alex Hales – who was dropped ahead of the World Cup due to an "off-field incident" – should not give up hope of returning to the fold despite not being given a central contract.
"The door isn't closed. He's a very fine short-format player," Giles said. "He needs to keep working hard and getting the runs - but if he does that, who knows?"
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