The company, which has operated in the city for more than 12 years, plans to shut the branch on or before the end of the firm's financial year on April 30.
It is part of a UK-wide restructuring plan, which could see a total of 251 staff made redundant in one of the British legal market's biggest round of lay-offs since the financial downturn in 2008.
Ten directors from Glasgow will transfer to the firm's Edinburgh site along with 30 other staff.
However, the remaining 45 workers, thought to include a mixture of solicitors and clerical workers, will face redundancy.
The company is also centralising its document production facilities, leaving a further 10 jobs at risk in Edinburgh.
The move follows a major review into the company's structure, including a consultation on the job losses and plans to sell off its defendant insurance practice.
A DLA Piper spokesman said: "Our collective consultation has concluded and we can confirm we will be closing our Glasgow office, divesting our defendant insurance practice and consolidating our current multi-site document production unit."
The spokesman added the firm will now begin individual consultations with staff facing redundancy.
It remains unclear what will become of the 10 employees in the capital at risk, as the firm plans to retain a small presence in each office to cover early morning and late night demands. This will be finalised over the next six months.
The firm confirmed it is in advanced discussions with two separate organisations who are looking to take over its defendant insurance practice.
Following the announcement of the consultation in November last year, a DLA Piper spokesman said the restructure was designed "to ensure that we are operating in a manner, in the locations, and across the practice areas that support both our strategic objectives and the needs of our clients".
Lorna Jack, chief executive of the Law Society of Scotland, said: "We understand that DLA Piper's Glasgow office will be closing and that some solicitors and support staff will transfer to their Edinburgh office, however we also understand their consultation process is ongoing.
"The continuing difficult trading conditions for firms does lead to uncertainty for staff. If any solicitor or employee of a legal firm would like to speak to someone, the Law Society's professional practice helpline is staffed by a team of qualified solicitors able to give confidential support and guidance at difficult times like these."