The centre-back has signed a two-year deal, with the option of a further 12 months, at Turf Moor following his departure from Scunthorpe.
Bedeau, 21, was linked with a move to Fratton Park earlier this summer – along with League One rivals, MK Dons, Oxford and Fleetwood.
The former Aston Villa man scored once in 37 appearances as Scunny narrowly avoided League Two relegation with a game to spare in the 2020-21 campaign.
Now after departing the Iron, Bedeau's opted to completed a switch to Burnley where he will link up with their development squad.
He told the Clarets' website: ‘I was really interested and excited when I heard about Burnley,” said Bedeau.
‘I have been around a little bit for a young player. I think it’s got me good experience and I’m just hoping to come and push on and develop here.
‘It’s another step and hopefully a big step. Hopefully, I do well here. I will work hard and hopefully get me where I want to be, which is in and around the first team and pushing that kind of way.
‘The set-up is top-class; the pitches, the gyms, the facilities are second to none.
‘It’s good to be able to develop yourself at somewhere like this. Villa was similar and I’m just excited to start here.’
Pompey have signed centre-half Clark Robertson on a free transfer from Rotherham.
The Scot penned a two-year deal on the south coast.