Cleveland — Jesse Jackson is changing his address but not his mission to alter traditional race relations and politics in the United States. In changing his official residence from Chicago to Greenville, S.C., he is seen by some black activists as following the trend of blacks moving back to the South, an area perceived as a new ''land of opportunity'' for blacks. And he is seen as breaking away his old Operation PUSH (People United to Serve Humanity), which lacked branches in a large number of cities - instead seeking to forge a Southern voting bloc boosted by local power bases.
The action, announced Wednesday near the conclusion of the Urban League conference here, has broad implications for the Rev. Mr. Jackson's career and for the Democratic Party this fall.
One thing the move surely does not signal is a return to the quiet life of a Baptist minister.
It keeps Jackson squarely in the political limelight as a national leader and voice for American blacks, and it avoids a possible loss in a tough Senate race against incumbent Republican Strom Thurmond. It positions him well - geographically and politically - for a 1988 run for president, or for launching a new regional or national political organization, or simply for expanding his constituency to include more whites and other minorities.
''Jackson's move to Greenville is great,'' says Vera Wilson of Providence, R.I., whose family lives in Greenville. ''Black people have a long record of progress in that city, a ... place for political achievement.''
For the Democratic Party, Jackson's decision not to run for the Senate means that instead of limiting his activities to South Carolina, he is free to lend his support - as much as he chooses - to the Mondale-Ferraro campaign.
He has not promised, however, to actually speak out for Walter Mondale and Geraldine Ferraro. ''I will work actively to defeat the Reagan-Bush ticket,'' Jackson says carefully. But he will help register voters and make personal appearances in behalf of the ticket.
The party's nominees for president and vice-president did not receive enthusiastic applause when they addressed the Urban League convention on Tuesday. The time, effort, and intensity Jackson exerts in the South in supporting the Democratic ticket could be crucial.
From his new geographical vantage point, Jackson will work toward the goal of electing 10 new black congressmen from the South, as well as placing more blacks in local elected positions.
If he succeeds in building a strong Southern coalition, he could:
* Create a fresh voting bloc that could support the Mondale candidacy at the polling place.
* Challenge the established Democratic Party in the South. ''We need to replace the 'boll weevils' (conservatives) of our party with new voices - black, brown, and liberal whites,'' Jackson says.
* Failing this, organize a new, independent wing of the Democratic Party to challenge established leaders, a source close to Jackson says.