Wroblewski, 59, said the stress of the past three months, including pressure from the aerospace company, politicians and his own union's national leadership, had put him in the hospital twice since Dec. 27.
The experience "changed my perspective on work-life balance," he said in a statement. "Your job should not destroy your health."
Wroblewski has served as president of Machinists Union District Lodge 751 since March 2007. He was re-elected in 2008, and again in 2012.
He announced his retirement to a union district council.
On Jan. 3, area Boeing machinists narrowly approved a contract in which they conceded some benefits in order to secure assembly of the new 777X in Washington state. The same machinists rejected a Boeing contract proposal in November. Wroblewski had argued against a second vote, saying the offers were too similar. National Machinists union leaders pushed for - and got -the second vote.
Political leaders including Gov. Jay Inslee had pushed for the second vote, citing concern about losing the Boeing jobs to another state.
Wroblewski called on union leaders and members to work together.
"We now have been awarded the right to build the 777X, and we must find a way to move this membership forward," he said. "I leave here honored to have served this membership, knowing that I always had the best interests of this membership guiding me."
In this month's vote, machinists approved an eight-year contract extension with a slim 51 percent vote in favor. Opponents of the contract opposed the idea of freezing the pension and moving workers to a defined-contribution savings plan. They also criticized increased health care expenses and slower wage growth.
Local union officials had urged their 30,000 members to oppose the deal, arguing that the proposal surrendered too much at a time of company profitability.
The union will select a replacement to serve out the remainder of Wroblewski's term, which runs into 2016, spokesman Bryan Corliss said