The comic actor, also known for his TV shows with Ben Miller, said voicing the character was "about as close to a dream job as you could wish for".
Armstrong takes over from Sir David Jason, who voiced the eye patch-sporting "DM" in ITV's original series from 1981 to 1992.
Kevin Eldon will voice trusty sidekick Penfold, Terry Scott's old character.
"When I am recording the episodes, I'll be making sure that at all times my eyebrows are at least three inches above my head," joked Eldon, known for his appearances in Big Train, Nighty Night and other comedy shows.
Other cast members include Shauna MacDonald and Morwenna Banks, while Dave Lamb - the voice of Channel 4's Come Dine With Me - will take on the role of narrator.
The new series, which will initially run for 52 episodes, is due to be broadcast on the CBBC channel in 2015.
Armstrong's Danger Mouse will have more gadgets at his disposal than the original, among them a multi-purpose "i-patch".
The actor previously voiced an alien super-computer in Doctor Who spin-off The Sarah Jane Adventures and Professor M in the animated series Tooned.
"As a lifelong fan of Danger Mouse, I was ecstatic just to know that the show was coming back," the 44-year-old said.
"To be actually involved with the reboot and to be taking DM out to a whole new generation is about as close to a dream job as you could wish for."
"We're all genuinely bowled over to have Kevin and Alexander on board as Penfold and the mighty DM himself," said CBBC controller Cheryl Taylor.
"They are both funny and fabulously talented performers and... will ensure that the series' considerable comedy credentials are bestowed on a new generation of fans."

Johnson was found guilty of sexual touching but cleared of one charge relating to another sexual act following a trial at Bradford Crown Court.
The court was told the grounds for appeal had been lodged on Thursday.
The former Sunderland winger is in court awaiting sentencing.
Johnson previously admitted grooming the girl and one charge of sexual activity.
Judge Jonathan Rose previously warned him he faced a "substantial prison sentence".

10 January 2017 Last updated at 16:08 GMT
"We are now in for a period of direct rule and I really do regret that, I think what the people of Northern Ireland want is stability but that has all been thrown in to very sharp relief," said Arlene Foster.

The two pools were confirmed on Monday after New Zealand accepted an invitation to play in Brazil.
The Dutch are ranked number two in the world with Germany third, while Ireland will also take on Argentina, India and Canada in Pool B.
"We're know how tough the tournament is and that we're in a tough group," said Irish coach Craig Fulton.
Argentina (sixth) and India (seventh) are above Ireland (12th) in the rankings with Canada 14th.
Pool A comprises Australia, Great Britain, Belgium, New Zealand, Spain and host Brazil.
"We will be focusing on improving as individuals, and as a squad and team come Rio," added Fulton.
"Our first training camp is in early January and we're looking forward to starting 2016 with a tough but enjoyable tour."
The match schedule for all pool games and the play-off stages will be announced in February.
Pointless host Alexander Armstrong will voice Danger Mouse when the much-loved cartoon hero returns to TV next year.
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Ex-England footballer Adam Johnson is to appeal against his conviction of sexual activity with a 15-year-old girl.
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Northern Ireland faces a "brutal" election following the resignation of Deputy First Minister Martin McGuinness, the outgoing first minister has said.
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Ireland's pool opponents at the Rio Olympics will include defending champions Germany and the Netherlands.