The union's leaders said they expected its 7,000 members to approve the agreement in March.
The House earlier this month approved the agreement, called a conference report, by a vote of 375 to 45.
The House also approved the agreement by a large margin.
Later in the day, union members voted to approve the agreement.
The union's negotiating committee approved the agreement in a 6-to-3 vote last night.
The board approved the agreement by a 9-0 vote, Phillips said.
Both countries parliament needed to approve the agreement before it could come into force.
Congress had approved the agreement and enacted it into law that year.
After a 30-day period of public comment, a federal judge will decide whether to approve the agreement, as expected.
Judge Rubin said he would approve the agreement later at a hearing.