The acquisition, announced in March, can move forward following FCA consent.
Edinburgh-based Standard Life has said the buy out of Ignis will aid the growth of its investments arm and strengthen its 'strategic positioning'.
The business will offer active management for institutional and wholesale clients, discretionary wealth management for high net worth private clients and outcome orientated products for maturing pension schemes and insurance companies.
Keith Skeoch, chief executive of Standard Life Investments, said: "The acquisition of Ignis is another step in Standard Life Investments' growth story, reinforcing our strong foundations, broadening our third party client base and increasing the range of investment solutions we offer.
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"This acquisition is entirely complementary, deepening our investment capabilities, broadening our third party client base and strengthening our strategic position from which to develop a business in the rapidly developing liability aware market. Standard Life Investments continues to perform very strongly.
"Our priority remains the continued delivery of strong investment performance and the highest level of clients Standard Life."
Standard Life has identified £50m worth of savings from the integration of Ignis with Standard Life Investments' operating platform, which it will carry out over three years.
The £390m deal will be settled in cash from Standard Life Group's existing internal resources.
Ignis had £59 billion of Assets Under Management as of 31 December 2013 excluding stock lending collateral. Ignis earned revenues of £150 million and generated EBITDA of £52 million in 2013.
Mr Skeoch, said: "The acquisition of Ignis continues the delivery of our group strategy to grow assets under management through enhancing our investment capabilities and expanding our offering to meet the changing needs of our customers.
"It will deliver enhanced earnings and cash generation and support future growth in revenues."