Barca said the agreements come after weeks of negotiations and include "temporary salary adjustments" in response to difficulties caused by the coronavirus pandemic.
Pique, who was sent off in the second half of Barca's 5-1 Champions League win over Ferencvaros on Tuesday, has signed an extension until June 2024.
The 33-year-old's future at Camp Nou had been in doubt after saying he would be the first to step aside following a humiliating 8-2 defeat to Bayern Munich in last season's Champions League quarter-final.
Pique has played 548 games for Barca, who say his extension is subject to him featuring in an unspecified number of games from the 2021-22 season.
De Jong, who created Ansu Fati's second goal in the win over Hungarian visitors Ferencvaros with a sublime scooped pass, extended his deal until June 2026 and has a termination clause of €400million.
The Netherlands international has featured 47 times for the club across all competitions since joining from Eredivisie powerhouse Ajax, scoring twice.
Barca goalkeeper Ter Stegen and defender Lenglet, meanwhile, have signed extensions until 2025 and 2026 respectively.
Ter Stegen, who has missed just eight LaLiga games since becoming first-choice goalkeeper at the start of the 2016-17 campaign, has a termination clause of €500m, while France international Lenglet's has been set at €300m.
Barca face bitter rivals and LaLiga champions Real Madrid in the season's first Clasico on Saturday before travelling to Juventus in the Champions League on Wednesday.