You're already on the team, so you've got a leg up where the company realizes they need design. Learning the language of business helps you tremendously. If you can show that design is an integrated part of successful companies, you will win them over in terms they understand by showing there is tangible value in the design process. Include the team in the design process early and often, and demonstrate that design thinking can have real monetary impact.
1. Do your research
Studies have shown design-centric companies outperform their counterparts by a significant amount. You should do your research and be able to show the value of design within the business terms. Data and research can be your crutch to show the financial value of design.
2. Brainstorms and design sprints
Get everyone in a room together and talk about the product. Help the realize design is all about how it works, then how it looks come last. Things like an abbreviated design sprint can help save the company money in burnt engineering cycles, and helps to get everyone on board.
3. Share early and share often
Share what you're working on early. Get input often from other members of the team. The more often they see their feedback integrated, the more likely they will feel connected to the design of the product.
4. Data is your friend
If you can quantify the value of design, do it. Run tests, study the data, look at the results of a redesign. Find ways you can tie your designs back to the business, because at the end of the day everything we design should be driving some business motive. (Side note - sometimes these motives are secondary or tertiary, such as a visual redesign ensuring your product looks fresh, which in turn will drive more usage, which in turn drives more revenue.