It takes two factors to make innovation real at an organization: concepts and culture. Work on both at the same time and the rest will emerge as a by-product of the process.
Without working on the culture while generating concepts, new thinking and new value-generating concepts will be rejected by the preset filters and default thinking of the organization.
On the other hand if you just work on the culture, but do not produce concepts that resonate in the market, you have created no new value.
Work on culture and concepts must be undertaken at the same time as part of an innovation journey that will assure a positive outcome. You have to work on the people in the business (culture) and on the market ideas (concepts: products, services, business model changes, initiatives, etc.), to transform into an organization that drives new results.
Do exercises and training to change the culture and work on concepts that are consumer- or customer-insight based.
Don’t worry about larger implications such as which department innovation will exist within, metrics for innovation, or how innovation will dovetail with the existing new product development process.
For the first 12-to-18 months keep the approach simple. Host a series of workshops to initiate the culture. Teach your people the methods and mindset of innovation, as tools for complex problem solving. Pick a small, multi-disciplinary team or two to work on a few projects. Generate new concepts that arise from market insights. Repeat.
Then, the right structure and definition for innovation for your company’s unique needs will naturally emerge.