NEW HAVEN, Conn. — Yale University has raised $3.88 billion amid tough economic times, finishing the largest fund-raising campaign in its history to help pay for its biggest expansion in decades, extend its international reach and make its school of music tuition-free.

The campaign exceeded its goal of $3.5 billion. More than 110,000 alumni, parents, friends, corporations and foundations contributed.

Yale began the campaign in 2006 with a nucleus of $1.147 billion, and by 2008, donations had reached $2.3 billion. While the global economic crisis brought a decline in giving for 2009 and 2010, contributions totaled more than $857 million in the final year.

The campaign will help pay for two new residential colleges expected to increase student enrollment by 15 percent, to 6,100.