July 8 (Reuters) - AMP Ltd will sell its global equities and fixed income (GEFI) business to Macquarie Group's asset management arm, the two companies said on Thursday, as the embattled wealth manager shrinks itself ahead of a spin-off.

The announcement comes after AMP, Australia's best-known manager of retirement savings, decided in April to spin off the private markets business of AMP Capital, the unit that holds GEFI, after failing to sell it to Ares Management Corp.

AMP shares, which are down nearly 30% this year, rose as much as 1.8% on Thursday, outperforming other financial firms and the broader market.

Macquarie Asset Management will shell out up to A$185 million ($138 million) for GEFI, which manages about A$60 billion in assets. Once completed, the Macquarie arm will see assets it manages rise to A$720 billion, the companies said in separate statements.

AMP, which continues to lose clients after three years of scandals, had embarked on an overhaul that included the sale of non-core assets in the company's hopes of becoming a simpler outfit.

The 172-year old company is trying to restore its reputation after a bruising public inquiry into the finance sector in 2018 revealed it had improperly charged fees and attempted to mislead regulators. Many top executives left and policyholders have been pulling their funds ever since.

"Our review of the GEFI business last year showed it had strong investment capabilities and performance but needed greater scale and broader distribution reach to compete effectively," James Georgeson, AMP Capital's acting chief executive officer, said.

AMP said it is assessing costs expected through the separation, which could close in the first quarter of 2022.

($1 = 1.34 Australian dollars)

(Reporting by Nikhil Kurian Nainan in Bengaluru; Editing by Maju Samuel and Sherry Jacob-Phillips)