The 19-year-old has signed a four-year contract at London Road for an initial fee of £200,000.
The transfer fee is spread over three years and could rise based on Ferdinand’s and Peterborough’s success, whilst the deal also includes a sell on fee.
“I am very grateful to Southend United for handing me my first team debut and it was a really enjoyable time at Roots Hall,” said Ferdinand on completing the move.
“I am really looking forward to playing for Peterborough, they play good football and I can’t wait to get started now.”
Ferdinand made his debut under boss Paul Sturrock on New Years Day 2011 in a 2-0 win at Oxford United.
That came after rising through the youth ranks at Roots Hall where he was originally a centre-back.
He went on to make 71 first team appearances scoring 10 goals for the first team.
Everyone at Southend United wishes Kane all the best for the future.