The emails are the first documentary evidence of a top Trump associate knowingly engaging with what they believed to be a Russian government effort to help Mr Trump in the 2016 election.
In one of the emails to Donald Trump Jr, the music publicist seeking to set up a meeting with a lawyer from Russia describes her as a “Russian government attorney”.
Mr Trump Jr was deeply involved in his father’s presidential campaign.
He posted the emails on Twitter on Tuesday and issued a statement describing it as an effort “to be totally transparent”.
The emails with publicist Rob Goldstone show Mr Trump Jr was told the Russian government had information that could “incriminate” Mrs Clinton and her dealings with Russia.
Mr Goldstone wrote to Mr Trump Jr the information “would be very useful to your father”.
He was working to connect Mr Trump Jr to Russian lawyer Natalia Veselnitskaya, who later met with Mr Trump Jr in New York at Trump Tower.
Ms Veselnitskaya has denied that she ever worked for the Russian government.
“If it’s what you say I love it especially later in the summer,” Mr Trump Jr replied to Mr Goldstone in one of a series of email exchanges the younger Trump posted to Twitter.
The email release followed days of evolving accounts from Mr Trump Jr about the nature of the meeting and its purpose.
The president’s son posted the emails only after they were obtained by The New York Times.
On Saturday, Mr Trump Jr described the encounter as being a “short introductory meeting” focused on the disbanded programme that had allowed American adoptions of Russian children.
Moscow ended the adoptions in response to Magnitsky Act sanctions created in response to alleged human rights violations in Russia.
A day later, Mr Trump Jr changed his account, acknowledging that he was told beforehand that Ms Veselnitskaya might have information “helpful” to the Trump campaign, and was told by her during the meeting that she had something about Mrs Clinton.
In his third description of what occurred, on Tuesday, he said he had believed the information he would hear about Mrs Clinton would be political opposition research.
He said that he first wanted to speak by phone, but that when that did not work out, he was told that the lawyer would be in New York “and I decided to take the meeting”.
“The woman, as she has said publicly, was not a government official,” Mr Trump Jr said in the statement on Tuesday.
“And, as we have said, she had no information to provide and wanted to talk about adoption policy and the Magnitsky Act.”