"I am very happy that you stand vindicated in the 2G case," Singh told Raja in a letter dated January 2, a copy of which was released to the media by the DMK today.
Former telecom minister A Raja and DMK MP Kanimozhi were on December 21 acquitted by a special court in the case.
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Raja said he had, in fact, brought a "revolution" in the telecom sector.
Singh, during whose tenure the alleged scam broke out, said Raja and his family "suffered greatly in this process (case)."
The senior Congress leader, a Rajya Sabha MP, said: "all your friends are greatly relieved that truth has prevailed."
He extended his new year greetings to Raja and members of his family.
Special CBI Judge O P Saini pronounced the judgment in the 2G scam which had rocked the Congress-led UPA-II government.
In its charge sheet filed in April 2011 against Raja and others, CBI had alleged that there was a loss of Rs 30,984 crore to the exchequer in allocation of 122 licences for 2G spectrum which were scrapped by the Supreme Court on February 2, 2012.