Roger Stone’s now infamous prediction involving John Podesta, a victim of the hacking campaign waged against Democrats during the 2016 presidential race, provided the latter with an apt response to the arrest of President Trump’s former election campaign adviser.

Mr. Trump’s longtime confidant and a member of his campaign through 2015, Mr. Stone was arrested Friday at his home in Florida early Friday in connection with a seven-count indictment related in part to the WikiLeaks publications.

“Rogers’s time in the barrel—and it’s headed over Niagara Falls,” Mr. Podesta reacted on Twitter.

In 2016, Mr. Stone used the same turn of phrase to jab Mr. Podesta.

“Trust me, it will soon the Podesta’s time in the barrel,” Mr. Stone tweeted on Aug. 21, 2016, shortly before the WikiLeaks website began publishing emails stolen from Mr. Podesta, the chairman of former Democratic presidential candidate Hillary Clinton’s campaign.

Russian military officers hacked Mr. Podesta’s personal email account, among other Democratic targets, and obtained sensitive material subsequently published online during the 2016 race by WikiLeaks, including internal Democratic National Committee emails released in late July, according to U.S. officials.

In a court filing unsealed Friday, special counsel Robert Mueller alleged that “a senior Trump campaign official was directed to contact Stone” after the release of the stolen DNC emails and determine “what other damaging information [WikiLeaks] had regarding the Clinton Campaign.”

Mr. Stone, 66, is scheduled to make his first court appearance later Friday morning.

“There is no evidence that I participated in or have any knowledge of any collusion with the Russians to effect the 2016 elections,” Mr. Stone said previously. “I had no advance notice of the content, source or timing of the Wikileaks publication of any material.”