The final phase of a long-awaited, multi-billion dollar Miami International Airport improvement project wraps up Tuesday.

Almost.

The new $180 million international arrivals center, a 400,000-square-foot facility on three levels, starts processing an average of 22,000 people a day after nearly three years of construction.

Tuesday’s opening essentially completes a $3 billion project to expand, beautify and modernize the airport’s north terminal that has been in the works since the mid-1990s.

Eleven years after the groundbreaking, all the construction and pardon-our-dust disarray — not to mention cost overruns, delays and embarrassments — are nearly history.

“It’s an amazing weight off my shoulders,” said Airport Director José Abreu, who has overseen the project since 2005.

Some of the most recent highlights during the extended renovation include the $130 million Concourse D skytrain, which opened in September of 2010 and the new $220 million baggage handling system, which started operating in March. Those followed the $1.1 billion overhaul of the South Terminal, where Concourses H and J include airlines such as Delta, United, Lufthansa and Air France.

This new federal inspection center should spare international travelers the long walks and disorganized lines that have plagued arrivals in the new north terminal, officials say.

“It’s just mass chaos normally,” said Rolando Suliveras Jr., port director for U.S. Customs and Border Protection at MIA. “We’re moving away from that. We’re going to controlled chaos.”

Although the new center is being hailed by federal customs and airport officials alike, it opens with some level of disappointment. The north terminal processing center, with 72 lanes and six Global Entry kiosks for pre-cleared travelers, was supposed to operate at the same time as the 36-lane central terminal’s facility in Concourse E to ease waits that can top two hours.

Eventually, Abreu said, that is the plan. But for now, until more Customs and Border Protection employees can be hired for both facilities, only the new north center will be open with at least 60 lanes open during peak times. It will serve passengers from American Airlines’ Concourse D as well as international flights that come in to Concourses E and F, including Iberia, British Airways and Virgin Atlantic.

Both Abreu and Suliveras said the airport’s international growth has come as a surprise; MIA is now the top airport for international flights. Through June, nearly 9.6 million international passengers traveled through MIA, an increase of 8 percent over the first half of 2011. That’s on top of 9 percent international growth last year. “Nobody, including me, could have forecast the kind of international passenger growth that we’ve experienced,” Abreu said.

As the growth is expected to continue with American Airlines adding additional international flights,more items remain on the to-do list.

Still unfinished in the new terminal are eight security stations to re-check connecting travelers and five baggage claim carousels in addition to the five opening Tuesday. Those last touches, held up by demolition of the terminal’s old baggage system, are expected to come online by March.

Even before those are finished, officials hope to shave 30-45 minutes off the total time for connecting travelers with the new facility opened.