The striker opted for a move to the Tractor Boys on a free transfer, penning a three-year deal.
Pigott had been on Danny Cowley's shopping list this summer following his departure from AFC Wimbledon.
However, the Blues had been braced to miss out on Pigott, who netted 54 goals in 157 outings during a prolific three-and-a-half-year stay at the Wombles.
The 27-year-old will remain in the third tier - but with Ipswich
Former Pompey boss Cook is conducting a major overhaul at Portman Road as they prepare for a third season in League One.
And he’s hoping Pigott can help fire Ipswich back to the Championship.
He will fill a void left by ex-Blues striker Oli Hawkins in East Anglia, who was deemed surplus to requirements and sold to League Two outfit Mansfield earlier this summer.
Pompey are still in the market for an additional centre-forward after missing out on Jayden Stockley.
The former Bournemouth marksman instead opted for a return to Charlton, having scored eight goals on loan at The Valley during the second half of last season.