Managing director Vinai Venkatesham will lead the Gunners on a day-to-day basis with technical director Edu and head coach Mikel Arteta heading up the club's recruitment process following Sanllehi's departure.
"Raul has made a big contribution during his time with us and will always be part of the Arsenal family. We thank him for all his hard work and expertise and wish him every future success," owners Stan and Josh Kroenke said in a statement on Saturday.
"We have no doubt that Vinai is the right person to take the club forward. He has shown outstanding leadership during the current crisis and is held in high regard internally and externally. We know everyone will rally round him so we can move forward successfully."
ESPN reported on Friday that the club had launched an internal investigation into their recruitment processes amid concerns that had been raised over several transfers including the club-record £72 million purchase of Nicolas Pepe from Lille.
There was surprise from individuals working for other clubs who became involved in preliminary talks with Lille about the amount the Gunners eventually paid for the 25-year-old.
The Gunners agreed to pay £20m upfront with a further £52m due in instalments over the next five years.
The depth of those commitments formed part of a wider drive to re-examine the decision-making process which led to such a big deal.
Arsenal denied that a formal investigation was underway and told ESPN that the club's wider efficiency drive contributed to Sanllehi's departure as well as the release of a raft of agents across Europe and 55 redundancies among non-playing staff.
Sources have told ESPN that the decision-making relating to several transfers had been reviewed in addition to the process for identifying talent, a point which former head of recruitment Sven Mislintat previously said had been a reason for his abrupt departure in January 2019.
Mislintat joined the club from Borussia Dortmund in November 2017 but quit 14 months later after Sanllehi's arrival and the decision to overlook the German for the technical director role which would later be given to Edu.
"We had different approaches. Previously we had a strong systematic approach to transfers, a mixture of watching things live as well as quality data and video analysis -- Arsenal actually owns their own data company," Mislintat told 11Freunde in July 2019.
"That meant that we acted independently, we knew about all markets and players in all positions that came into question. However, the new leadership work more strongly with what they are offered from clubs or agents through their own networks."
Arsenal also denied that Sanllehi's departure was related to his relationship with agents.
The club has worked closely with Kia Joorabchian lately, having completed business with three of his clients. Willian joined on a free transfer from Chelsea while Cedric Soares' loan deal from Southampton was made permanent and David Luiz's contract was renewed.
Under the revised structure at the Emirates, Edu will work with Arteta to identify players going forward with Venkatesham responsible for managing budgets.
Contract expert Huss Fahmy will then seek to actively negotiate with clubs to sign targets all with oversight from the board.
"I'm proud and pleased with the contribution I've made at Arsenal over the past three years, and look forward to enjoying the club's future success. Arsenal is a true footballing institution," Sanllehi said in a statement.
"I am proud to have been part of its history and I thank Stan and Josh Kroenke for this opportunity. Working with Vinai, we have built a top team for the future. Mikel has made an extremely positive impact since his arrival and has formed a strong team with our technical director, Edu.
"The academy is in very safe hands with Per, and Huss Fahmy is a talented and highly capable leader of our football operations. Personally, I now look forward to taking some time off and spending time with family and friends before setting to work on a new challenge and cheering Arsenal on to great things."
Corporate lawyer Tim Lewis, who joined the board as non-executive director at the beginning of July, was an influential figure in the review of Arsenal's processes, helping to identify various areas for cost-saving.