Van Morrison's former primary to become a special school
Belfast was identified as one of the areas where there was a particular pressure on school places.
Mr Pengelly said that some mainstream schools could be instructed to enrol more SEN pupils.
Gary Forbes
The chair of Greenwood House's governors Gary Forbes said the special school's move would help parents and pupils.
"This will mean that we can offer a place to children up to Primary 7, which gives parents a degree of comfort and assurance about their children's education and development," he told BBC News NI.
"It'll really help families, and we're also looking forward to expanding to use the old Elmgrove site."
"We want to thank officials from the Education Authority for their support," he added.
"The Board of Governors also want to pay tribute to our principal, Lorriane Thompson, and wonderful staff for all their hard work and dedication."
In a statement to BBC News NI, a spokesperson for the EA said: "As part of ongoing efforts to increase capacity across the school estate, EA has been working closely with Greenwood House to expand its provision from age 3 to age 11 from September 2026, utilising the old Elmgrove site which will be refurbished as part of the plans."
"The transition process will start this year and will help the overall position," they continued.
As well as Sir Van Morrison, other former pupils of Elmgrove Primary include the late Northern Ireland footballer and manager Billy Bingham and unionist politician David Ervine.
Meanwhile, the EA has confirmed plans to create a new special school at the site of the former Orangefield High School in Belfast.
BBC News NI understands that could mean a number of existing special schools being relocated to the site of the former high school in east Belfast.
The first integrated Irish language primary school in east Belfast, Naíscoil na Seolta, has previously said it is also interested in a long-term move to the Orangefield site.