Celta, who reached the last 16 of the Champions League in 2004 and won the Intertoto Cup three years earlier, have 85 points from 42 matches, six behind Depor, who were 1-0 winners at Villarreal B and set a second-tier record of 91 points.
Real Valladolid, Alcorcon, Hercules and Cordoba finished the season in third through sixth respectively and will play off for the final promotion spot, with Almeria just missing out a point behind Cordoba in seventh.
Celta's return to La Liga may help the club tackle the severe financial problems that have forced it into administration as they are likely to reap considerably more from selling audiovisual rights next season.
A study by a professor of accounting at the University of Barcelona published recently showed Celta had debts of 51 million euros in the 2009-10 season compared with assets of 52.4 million.
Celta and Cordoba both needed only a point to secure their objectives and appeared happy to settle for the draw from the start, prompting the headline on Marca sports daily's live coverage of the match "Non-aggression pact".
Racing Santander, Sporting Gijon and Villarreal were relegated from La Liga last season.