Thornberry, who speaks on foreign affairs matters for the party, failed to secure the nominations she needed to progress to the final ballot of party members. By the midnight Friday deadline, Thornberry had 31 nominations from local constituency parties, two shy of the number required.
The three remaining candidates, Keir Starmer, Rebecca Long-Bailey and Lisa Nandy, had already obtained the nominations they needed.
They now will go on to the online and postal ballot of party members and registered supporters. That contest opens on Feb. 24 with the winner being announced at a special conference on April 4.
Labour suffered its worst defeat since the 1930s in December's general election, which saw Prime Minister Boris Johnson's Conservative Party win a strong majority in parliament.
Many reasons have been cited for Labour's big defeat including the leadership of Corbyn, a veteran left-winger who was seen to have put off mainstream voters. The party's unclear position on Britain's departure from the European Union and cases of anti-Semitism among some members have also been cited as factors in Labour's defeat.