In his letter, the 43-year-old says Chief Minister Arvind Kejriwal, the chief of AAP, reneged on promises he made to score a blockbuster victory in the Delhi election in two years ago.
Mr Prakash's list details his concerns on rural Delhi, Shahbad Diary and Bawana, his constituency,
"Saddened by the failed promises, grand claims, let-downs and the unsuccessful government, I am resigning today to keep the faith the voters have in me," Ved Prakash writes.
He alleges that the AAP government, which came to power on the back of its pledge for clean governance, "has taken no concrete step" in two years to make good on it.
Ved Prakash's resignation was such a big shock to AAP that the party cancelled a press conference at the last minute yesterday.
Sources say the lawmaker did not answer Mr Kejriwal's phone call. Next they knew, he was sitting in the BJP office.
Ved Prakash had joined AAP in 2015 after quitting the BJP.
Speaking to reporters about his decision to return to the BJP, he said he "felt suffocated" in AAP.
He also claimed that Mr Kejriwal was unaware of what is happening in his party. "I have written to Kejriwal many times but he is surrounded by people who are misleading him. The government is running on laptop."
AAP has accused the BJP of trying to lure its lawmakers away.