The opening batsman will be in charge of the tourists throughout the tour following Andrew Strauss' decision to take a break.
The Essex left-hander has led his country in international cricket just once before, a Twenty20game against South Africa that ended in a heavy defeat.
On that occasion he was a late stand-in for the injured Paul Collingwood, but this time around Cook is very much the man at the helm for the entire trip.
Proud moment
"It's a hugely proud moment for me, but that's beside the point," he said ahead of the opening one-dayer on Sunday.
"It is a proud time but I'll be even prouder if we go out and play some good cricket, execute our skills well and are good enough to win.
"Being comfortable with the captaincy is something that comes with time in the job as you gain in confidence.
"As time goes on you feel more settled and less new in the role.
"The first international (of a tour) is different, there's a bit more pressure on but I'm really looking forward to that pressure."
Cook has enjoyed success both as a captain and as a batsman so far in Bangladesh, registering back-to-back half-centuries in a pair of warm-up wins.
Craig Kieswetter seems likely to be the skipper's opening partner in Dhaka having only been added to the one-day squad last weekend.
The Somerset wicketkeeper-batsman starred for the England Lions in Twenty20 action this winter and, after completing his qualification period, smashed 143 against a Bangladesh Cricket Board XI in Fatullah on Tuesday.
His fine form could lead to him taking over behind the stumps from Matthew Prior, though England may also opt to pick both in their starting XI.
The other selection issues for team director Andy Flower ahead of the first ODI concern the structure of the bowling attack.
There is the option of playing James Tredwell, who picked up 2-17 against the BCB XI on Thursday, to compliment fellow spinner Graeme Swann on what is expected to be a slow, low pitch.
Whichever team England pick, Cook has warned the players not to let complacency creep on the eve of the three-match series.
"It's been a good week so far. We've played some very good cricket in the warm-up games and improved in the areas we wanted to," he said.
"But that doesn't count for anything before the first international game so we have to come out firing and play the cricket we have been playing for the last eight months.
"The lads have built up nicely with the matches (against Pakistan) in Dubai and the two warm-ups here, but everyone has talked about how we have to be on our game. There's no complacency."
Home advantage
Bangladesh will be hoping to register a win over England to complete a full set of international scalps, with captain Shakib Al Hasan hoping home advantage can tip the balance in the Tigers' favour this weekend.
"We will try to win at least one game," said the all-rounder.
"Hopefully we can win two to win the series but we will target our first match and then go step by step. If we play to our ability, it's possible
"Obviously when playing at home we know we are a very good team, with home advantage. We are definitely a better team at home."
The hosts are without captain Mohammad Ashraful after he asked to be rested following an indifferent run of form with the bat.
