"I'm a little dazed and grateful for the support I got," she told news agency TT.
The 58-year-old bishop is married to a priest and has two children.
Jackelen, who was ordained in 1980, said it was not so strange for the church to choose a woman leader.
"It doesn't come as such a surprise," Jackelen said. "We have had female priests for over 50 years."
About two thirds of Swedes are members of the Lutheran Church of Sweden, which separated from the state in the year 2000.
Sweden follows in the footsteps of other Lutheran churches in the US, Canada, Germany and Norway which have appointed female leaders.
"It was about time," Anders Wejryd told TT.