The Foyle MP used parliamentary privilege to identify Solider F during a debate in the House of Commons earlier this week.
He said he had since received deaths threats online and via email.
Mr Eastwood said he had passed details of the threats to police.
The PSNI was treating the threats seriously, the SDLP leader said, but he added he would not be deterred from standing up for the Bloody Sunday families.
The Foyle MP named Soldier F during a debate in the House of Commons on the Armed Forces Bill on Tuesday afternoon.
The speaker of the House of Commons Sir Lindsay Howell has since said Mr Eastwood “broke no rules”.
Soldier F is facing two murder charges over the killings of William McKinney and James Wray and five attempted murder charges for his actions on Bloody Sunday in 1972 when 13 people were shot dead by paratroopers.
He was granted anonymity after the judge hearing the case concluded “a real risk does exist” to the life of Soldier F and he is right to “feel genuine fear”.
But the Public Prosecution Service (PPS) said it planned to withdraw the charges after reviewing the case and decided statements were no longer admissible evidence.
Leave has been granted for a judicial review into the PPS’s decision not to proceed with the prosecution.
The case is due to be heard in SeptemberTags: