Tyagi, who represents Bihar, fills the vacancy caused due to resignation of Upendra Kushwaha on January 4 following differences with Bihar Chief Minister Nitish Kumar.
Earlier, Kushwaha was suspended from JD-U for anti-party activities and was facing disqualification threat.
Patil was elected in a bye-election in Maharashtra necessitated by the death of former Union Minister Vilasrao Deshmukh.
Patil had left Congress in the mid-90s when P V Narasimha Rao and Sitaram Kesri were at the helm, alleging the leadership was targeting people close to the Gandhi family.
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Rajya Sabha Chairman Hamid Ansari also informed the House that he has accepted the resignation of lone Rajya Sabha member from Meghalaya Thomas Sangma (NCP), who quit the Upper House to contest Assembly election from North Tura.
Home Minister Sushilkumar Shinde informed the House about the imposition of President's rule in Jharkhand and laid a copy of the proclamation under Article 356 of the Constitution in this regard on the table of the House.
Ansari later adjourned the House after making obituary references to seven former members - Sushila Shankar Adivarekar, Charanjit Chanana, Krishnand Joshi, Nand Kishore Bhatt, Nripati Ranjan Choudhury, Narain Prasad Gupta and Radhakishan Malaviya.
He also condoled the death of 38 pilgrims at Allahabad on February 10.