"I'm very pleased that we can resume our normal diplomatic ties," Swedish Foreign Minister Margot Wallstroem told reporters.
The announcement followed a visit to Riyadh by Swedish government envoy Bjoern von Sydow on Friday, where he met with Saudi Arabia's King Salman.
According to Swedish news agency TT, von Sydow relayed messages from Sweden's King Carl XVI Gustaf and Prime Minister Stefan Loefven during the meeting.
"We can ... welcome the Saudi ambassador back to Sweden (and) we can clear up the misunderstanding that we have insulted the religion of Islam," Wallstroem added.
Riyadh recalled its ambassador on March 11, accusing Sweden of "flagrant interference" in its affairs after Wallstroem told parliament in February the oil-rich state was a "dictatorship" that violated women's rights and whipped bloggers, a practice she in January had called "medieval".
Saudi laws are based on sharia, a moral and religious code.
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Around the same time Sweden unilaterally cancelled a long-standing military cooperation deal between the two countries, prompting Saudi Arabia to prevent Wallstroem from making a speech on human rights to the Arab League.
Saudi Arabia proceeded to freeze Swedish business visas to the Gulf kingdom, while its neighbour the United Arab Emirates also recalled its ambassador to Stockholm.
Wallstroem has throughout the diplomatic row maintained that she has the support of the Swedish people in expressing her position.
And she told daily Expressen on Saturday: "I do not regret my choice of words."
Von Sydow said he had stopped short of an apology during his talks with the king.
"I said we were very sorry if there were feelings of misunderstanding about what was said from the Swedish side, and said that we want to have a dialogue," he said.
"Sweden wants to have a dialogue on all questions, including those where we have different opinions," he added.