West Coast backup is 'epic': Port boss

Several months to clear 'epic' port backlog: Pro

It will take West Coast ports about two months to process backlogged work and return operations to normal after a labor dispute led to widespread delays, the Port of Long Beach's CEO told CNBC on Monday.

"It's an amazing congestion problem. It is epic proportions from our perspective," Jon Slangerup said in a "Squawk Box" interview.

A group of shipping companies and the powerful dockworkers union reached the tentative deal on Friday after nine months of negotiations, settling a dispute that disrupted the flow of cargo through 29 U.S. West Coast ports and snarled trans-Pacific maritime trade with Asia.

Read MoreWest Coast ports, union reach tentative labor deal

The Port of Long Beach was running at full strength on Saturday night and Sunday, said Slangerup. His team is doing everything it can to align truckers and rail operators and to make additional space available to begin staging containers and getting them off the docks, he added.

However, the priorities for processing cargo will be set by ocean carriers and the cargo owners themselves, and the docks can only fulfill those priorities as they are dictated.

Negotiations reopen West Coast ports: Secretary Perez

West Coast dockworkers are likely to approve the new contract after a committee that represented them unanimously approved the terms of the deal, U.S. Labor Secretary Thomas Perez said on "Squawk Box."

"I think that's a good start and I have all the confidence in the world that when the rank and file take a look at this they will see that this is a good package for them and that they should move forward," he said.

The agreement was reached three days after Perez arrived in San Francisco to broker a deal with the help of a federal mediator who had joined the talks six weeks earlier.

Slangerup said he was grateful to Perez, whose involvement made the difference in reaching an accord. He added that the deal should head off the chance of disruptive disputes arising in the near future.

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"It's a five-year agreement so it gives us some stability," he said. "Also, the fact of the matter is there were a number of issues addressed in this contract that won't be issues next time, so I'm hoping that we have some good solid progress and labor peace for the foreseeable future."

Talks had stalled over demands that the union be allowed to fire arbitrators in workplace grievance proceedings. The new deal lays out a process in which a panel will hear disputes, rather than single arbitrators.

The 20,000 dockworkers covered by the tentative five-year labor accord have been without a contract since July. The deal reached on Friday must go before union members for ratification. The vote will most likely take place in April.

The International Longshore and Warehouse Union and the shippers' bargaining agent, the Pacific Maritime Association, agreed to fully restore all port operations by Saturday evening.

—Reuters and CNBC's Katie Cramer contributed to this report.