Hanescu's winning score was 6-3, 6-4.
Andreev was playing in his second match of the day, having completed a rain-delayed 7-6 (7-2), 5-7, 7-6 (7-5) semifinal win over Guillermo Garcia-Lopez before taking on Hanescu.
Hanescu, ranked No. 80 in the world, was in his second finals match. In the other, he lost to Gilles Simon last year in Romania.
"Last year I had a great opportunity to win my first title in the Bucharest final, as I led 6-4 and by a break of serve," Hanescu said. "Today when I got to a similar stage I was thinking this can't happen again. Not two times in a row. I had to stay strong mentally and I served well towards the end of the match."
Andreev has won three times on tour, all in 2005.
Notable deaths of 2014 [PHOTOS]