However, he and NHS Scotland clinical director Professor Jason Leitch acknowledged there are still some aspects which need further attention.
Prof Leitch said some hospital services may need to be centralised in order to enhance the quality and safety of care.
The probe into NHS Lanarkshire's hospitals began last summer after routine checks flagged-up high death rates at two of its three hospitals.
In December a damning report raised a number of serious issues including gaps in medical cover, inadequate checks on deteriorating patients and nurse shortages.
Yesterday Mr Neil told Holyrood's Health and Sport committee: "I am pleased that the focus on patient safety and quality of care has increased significantly in recent months, and I am reassured that this focus will continue.
"In particular, the creation of a dedicated patient safety team, led by an experienced Head of Patient Safety, is helping to embed patient safety throughout the organisation." Controversial plans to cut the number of A&E departments in Lanarkshire from three to two were reversed by the SNP when they formed a minority government.
While the Scottish Government is not revisiting this debate, Prof Leitch said yesterday: "In the longer term they may need some redesign of services. It may be that the best thing for safe and quality care is some services will not be provided on all three sites."
The current spread of orthopaedic services had already been flagged-up as requiring attention by Healthcare Improvement Scotland, who carried out the mortality rates review.
An extra £3.1m is being invested in frontline nurses in Lanarkshire as a result of the review, according to Mr Neil. The rotas for medical staff have also been examined with government support officials.
However, Prof Leitch said: "There are still pockets of challenge as there are throughout Scotland, particularly with senior decision makers, where recruitment is a difficulty."
Ian Ross, NHS Lanarkshire chief executive, said: "We fully accepted the recommendations from the review and regret that we did not always meet the high standards of care we want for our patients."
He said the board had acted immediately to develop an action plan following the recommendations and appreciated the support they had received.