You have the option to cap selected borders, but it will create a network of invisible triangles that in many situations could be no ideal, specially with complex holes. But you should check first if it is enough for you selecting the border and cap. After that you can use the cut tool if you need some support loops to avoid too many geometry distortions. You could cap it by sections also to simplify the problem using bridge edges.
As better alternative you have 1 free script and 2 paid ones. They will try to create a logical net of quads and conform to the hole shape. You can find them easily in internet search following his name. Because the complexity of your hole I'm not sure if they are going to be a magical one click tool and could need some digging.
Free
- Rapid tools, Qcap. Included in a set of scripts. The simpler one but can be OK in many cases
Paid
- Quad Cap Pro from Silaghi, a modifier with plenty of options
- Miauu 2 package, cap holes. With lots of other scripts included. Less features.
Both are relatively cheap, specially Miauu 2 as include many others.