Mr Sirisena set free Sivaraja Jenivan at a ceremony to mark his first year in power. The men shook hands on stage.
Jenivan was arrested in 2006, but was only convicted - and given a 10-year prison sentence - last year.
The Tamil Tigers' 25-year fight for an independent state in the north of the country ended in their defeat in 2009.
Jenivan, now aged 36, was taken into custody in April 2006, accused of being part of an attempt a year earlier to kill Mr Sirisena, who was then a senior cabinet minister.
He was sentenced by the Polonnaruwa High Court only in July last year.
In pardoning him, Jenivan's lawyer said the president had taken into account the fact that the former militant had already been detained for 10 years.
At his anniversary celebration, President Sirisena pardoned and blessed Jenivan, touching him on the head and shaking his hand in front of a crowd.
He later tweeted a photo of himself on stage with Jenivan, with a caption reading: "Ordered Presidential Pardon to a prisoner who was serving time for attempting to assassinate me in 2005".
The Liberation Tigers of Tamil Eelam (LTTE) was a separatist rebel group led by Velupillai Prabhakaran who, to his followers, was a freedom fighter struggling for emancipation for the minority Tamils.
The group used suicide bombings to attack Sri Lanka's capital, Colombo, in the 1990s, killing high-profile figures including former Sri Lankan President Ranasinghe Premadasa.
In the closing stages of the war in 2009, both sides were accused of committing atrocities.
Upon taking power, Mr Sirisena pledged a truth and reconciliation commission to investigate the claims of abuses.
In October a government-led inquiry found that there were "credible" allegations that the army had committed war crimes during the conflict.
In the same month, 223 Tamil prisoners went on hunger strike demanding to be freed. Some have been released but most remain in prison.
Sri Lanka's president, Maithripala Sirisena, has pardoned a former Tamil Tiger militant convicted of trying to assassinate him more than a decade ago.