BJD candidate Rita Sahu trounced her nearest rival, Ashok Panigrahi of the BJP, by 41,932 votes.
The Election Commission said Sahu polled 1,02,871 votes compared to 60,939 votes secured by Panigrahi.
Pranaya Sahu of the Congress, which had held the seat three terms in a row, came third with a paltry 10,274 votes and lost his deposit in the constituency which was regarded as the party's bastion.
"He (Harichandan) has sent his resignation letter to the Congress president today," All India Congress Committe General Secretary and Odisha in-charge B K Hariprasad told PTI over phone.
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Asked whether the resignation has been accepted, Hariprasad said, "No decision has so far been taken on his resignation. The Congress president will decide what to do."
The BJP had polled 30,001 votes from Bijepur in the 2014 Assembly elections.
While the BJD's vote share jumped to 56.78 per cent from 31.88 per cent in 2014 Assembly elections, votes polled by the BJP also increased to 33.53 per cent from 18.11 per cent.
As many as 1,684 voters opted for the NOTA (None Of The above) option in the bypoll held on February 24, EC's returning officer Tapiram Majhi said.
The by-election was held following the death of three-time Congress MLA Subal Sahu in August last year.
The BJD fielded Subal Sahu's widow as its candidate, while Panigrahi left the BJD and contested as a BJP nominee.
Chief Minister Naveen Patnaik said the Bijepur by-poll result would have an impact on future elections in Odisha.
"I would like to express my deep gratitude to the people of Bijepur Assembly constituency for having showered their blessings on the BJD," Patnaik said.
Asked about pre-poll violence in Bijepur, he said, "People will not stand for violence in a democracy."
Odisha's people were peace loving and has rejected the politics of hatred and violence, Patnaik tweeted.
Following her win, Rita Sahu said, "I will work for the all-round development of the people in our area and strive hard to fulfil my husband's dream."
Asserting that the BJP was unable to properly present before the people the "inefficiency and misrule" of the BJD, Pradhan claimed the bypoll result amply demonstrated that there existed a tactical understanding between the BJD and the Congress.
About the poor show of the Congress candidate in Bijepur, B K Hariprasad said, "We could not match the money and muscle power of both the BJD and the BJP.