The Crimean Bridge, at 19 kilometres (nearly 12 miles) will be Europe's longest, overtaking Lisbon's Vasco da Gama Bridge.
Built at a cost of 228 billion rubles ($3.7 billion), the new structure, connects the southern Krasnodar region with the Crimean city of Kerch, spanning a strait between the Black and Azov seas.
Ukraine has condemned the project, which was personally championed by Putin, saying construction has damaged the environment and that larger ships will be unable to get through to its ports on the Azov Sea.
Meanwhile, Ukraine's security service raided the offices of Russian state media in Kiev and detained one journalist, moves the chief editor of Russia's RT television suggested were linked to the bridge opening.
The chief editor of the Kremlin-funded channel, Margarita Simonyan, wrote on Twitter that "Kiev decided to take revenge on us for the Crimean Bridge," after the raids on the offices of RIA Novosti state news agency, which is part of the same media group as RT.
European Union and US sanctions have targeted those involved in building the bridge, principally Putin's close ally, businessman Arkady Rotenberg, whose company Stroygazmontazh won the construction contract.
The annexation of the peninsula in 2014 was condemned by Kiev and the West as an illegal land grab but applauded in Russia.
Currently the peninsula is hard to reach from southern Russia with long queues of vehicles often forming to board ferries, which cannot always run in winter storms, so the easiest way across is to fly.
Because of blocks imposed by Kiev, in addition to Western sanctions, a large amount of food is currently shipped to the peninsula from Russia, so the bridge will play an important role in reducing the region's reliance on sea transport.
Crimea is popular among Russians as a summer holiday destination and Putin said in March he would like the bridge to be ready for the season.
Another unsuccessful attempt was made in the 1930s under Joseph Stalin. During World War II the occupying Nazis also began building a bridge, but abandoned the project.
"Today, both in a practical sense and from a symbolic point of view, is an extremely important day," he added.
The four-lane road bridge is opening ahead of schedule as it was due to be completed in December. Once it opens for traffic on Wednesday, it will be able to carry up to 40,000 cars per day.
The railway bridge is not yet finished and has a deadline of the end of 2019. A connecting highway from Kerch to the regional capital of Simferopol is set for completion in 2020.
Ships will be able to pass through an arch of the bridge that is 35 metres (115 feet) high in the deepest part of the strait. It is also designed to withstand ice floes in winter.
The construction is one of Putin's legacy projects, after the massive renovation of the Black Sea city of Sochi for the 2014 Winter Olympics and the 2012 opening of the world's longest cable-stayed bridge in the far eastern city of Vladivostok.
In March elections, Russians overwhelmingly voted for Putin to serve a fourth Kremlin term, but an opinion poll by the independent Levada centre found 45 percent of the population think he is failing to ensure that the country's oil and gas revenues trickle down to benefit ordinary people.
Nevertheless, a Levada poll in March found 70 percent of Russians thought taking Crimea had been beneficial.
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