Webster, 21, made 81 appearances for Pompey, having made his debut in 2012 against West Ham in the Championship.
The fee is a record for a player under Town boss Mick McCarthy and Webster has signed a three-year contract.
Clarke, 19, spent last season on loan at Fratton Park and has now agreed a three-year deal.
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Ipswich have signed Portsmouth defender Adam Webster for a fee believed to be about £750,000, with defender Matt Clarke going the other way.