Trump Jr., the president's eldest son, said in a statement that he released the back-and-forth "in order to be totally transparent."
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 Trump in the 2016 election.
In the first email of the chain, dated June 3, 2016, Goldstone wrote that "the crown prosecutor of Russia met with his father ... and in their meeting offered to provide the Trump campaign with some official documents and information that would incriminate Hillary (Clinton) and her dealings with Russia."
Goldstone said that the information "would be very useful for your father."
"This is obviously very high level and sensitive information, but (it) is part of Russia and its government's support for Mr. Trump," Goldstone wrote.
"If it's what you say, I love it, especially later in the summer," Trump Jr. responded in a subsequent email.
The president's son said he believed the information Goldstone had on Clinton was comprised of political opposition research.
Goldstone said he was asked to contact Trump Jr. about the information by Russian pop star Emin Agalarov, who Trump Jr. met during the 2013 Ms. Universe Pageant in Russia. In an email dated June 7, Goldstone said that he was asked to schedule a meeting between Trump Jr. and a "Russian government attorney."
Goldstone was working to connect Trump Jr. to Veselnitskaya, who later met with Trump Jr. in New York at Trump Tower. Veselnitskaya has denied that she ever worked for the Russian government.
"The woman, as she has said publicly, was not a government official," Trump Jr. said. "And, as we have said, she had no information to provide and wanted to talk about adoption policy and the Magnitsky Act."
The email release followed days of evolving accounts from 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.
U.S. stocks plummeted in the aftermath of the email release, according to Reuters.
The Associated Press contributed to this report.