The milestone means the Government has to issue an official reply.
There have been renewed calls for the former prime minister to face legal action after the Chilcot Report delivered a scathing verdict on the “flawed intelligence” and “far from satisfactory” legal basis for war.
The petition says: “The Chilcot Report has presented a range of evidence that demonstrates that Parliament and the country were misled by Tony Blair in the run-up to the war in Iraq.
“Parliament should now agree a process by which it can hold the former prime minister to account.”
If the petition reaches 100,000 signatures it will be considered for a debate in Parliament.
SNP MP Tasmina Ahmed-Sheikh said: “This is a significant milestone for this parliamentary petition. Now it has received 10,000 signatories the UK Government is required to make a formal response on the issue.
“The next step is to press for 100,000 supporters, which would lead to a parliamentary debate on the topic.
“In the meantime, I’ll continue to work with MPs from across the House Commons who want to see Parliament act to address this serious issue.
“If we are to retain the public’s confidence in Parliament, we must hold Tony Blair to account for the misleading statements he made in the run-up to the war in Iraq.”
Plaid Cymru Welsh Assembly member Adam Price said: “As the damning Chilcot Report clearly demonstrates, Blair is guilty of a litany of errors and failures.
“He must face his day of reckoning if justice is to be served to all of those who suffered at his hands.”
Meanwhile, families of British troops killed in the Iraq War have raised nearly £125,000 as they pursue legal action against Mr Blair and other leading officials.