Sunderland have completed the signing of Celtic right-back Adam Matthews for a fee of £2million.
Diego Poyet is determined to establish himself in Slaven Bilic's West Ham side this season and avoid another loan spell.
The pair joined Posh on loan from Crawley and Macclesfield respectively with a view to making their moves permanent in the summer and that has now happened.
Barnett, who was named in the npower League Two team of the year for his goalscoring exploits at Crawley prior to his February switch, adapted to Championship football quickly.
The 26-year-old striker scored four times in his first six appearances for Peterborough, including a last-gasp equaliser to earn a 1-1 draw at Doncaster on his debut.
Defender Brisley, 22, who moved to London Road on transfer deadline day in January, made 11 appearances for Posh after making his debut in a 3-1 home win over Blackpool in March.