The House voted 257-156 Thursday to approve legislation giving $20,000 tax-free payments to thousands of Japanese-Americans who were rounded up and sent to internment camps at the outbreak of World War II.

The bill now goes to the White House, where President Reagan has said he will sign it, ending "a sad chapter in American history."With the money will come an apology from the U.S. government for having forced about 120,000 Japanese-Americans - both citizens and resident aliens - from their homes and jobs following the Japanese attack on Pearl Harbor, Hawaii, on Dec. 7, 1941.

The payments will begin in about a year and will total about $1.25 billion. Individual payments to the estimated 60,000 surviving internees will be made over a 10-year period.

In return for the money, those who qualify must agree to drop any legal claims against the government stemming from the internment.

The legislation also authorizes payments of up to $12,000 each for surviving members of the Aleut Indian tribes who were removed from the Aleutian Islands during the Japanese attack there in 1942.

Rep. Norman Y. Mineta, D-Calif., who himself spent part of his youth in an internment camp in Wyoming, said "this legislation touches all of us, because it touches the very core of our nation."