Chavez has angered Washington by criticising George Bush, the US president, while the more subdued da Silva has maintained good relations with the White House.
The bridge, near the Venezuelan city of Peurto Ordaz, is the second to be built across the Orinoco and will boost trade between the two nations.
It cost $1.2 billion to build.
Da Silva said: "I come to Venezuela today more convinced than when I came a few years ago that it was worth building an alliance between Brazil and Venezuela.
"And you, Chavez, have shown that economic growth can be partnered with social justice."
The Brazilian president's trip to Venezuela is his first international visit since winning a resounding election victory last month.
Chavez said he would repay the visit if re-elected in polls next month.
"I will go to Brasilia on December 7, when I am re-elected, following Lula's example," Chavez said.
Polls give Chavez a comfortable lead of between 18 and 35 points over his rival.