The North Jersey Transportation Planning Authority yesterday approved a proposal by Gov. Jon S. Corzine to spend $1 billion in federal highway funds over 10 years on a new commuter rail tunnel under the Hudson River. The tunnel is expected to cost $7.5 billion to build, and officials have raised $3 billion of that, including the funds approved yesterday. Supporters say the tunnel will double rail capacity between New York City and New Jersey and will reduce highway congestion. New Jersey will also apply for funds from the Federal Transit Administration for the project. Construction of the two-track tunnel is expected to begin in 2009 and end in 2016. To make up for the diverted federal highway funds, New Jersey will use $1 billion from its Transportation Trust Fund on state road work.