A few days after getting out of the hospital, Derek started his job as head of neuro at Seattle Grace. At first there was a little awkwardness with him dating an intern and people accusing the couple of special treatment, but it turns out that Meredith has a knack for being intimidating and a little terrifying when she wants to be, so the accusations stopped. At least the accusations to her face stopped. After a while they stopped all together as people got used to the idea of them being an item.
There were some struggles in their relationship as there are in every relationship. She thought Derek was being stupid when he continued to refuse to talk to his family when they finally decided they missed him. He thought she was being hypocritical since she had recently avoided her father who decided to reach out to her. In the end they made up and wound up both reaching out to their family members. Derek is not super close with them anymore but he is happy with the group of friends and lovely spouse he has now. And his best friend eventually followed him to Seattle when he realized Derek wasn't going to be coming back.
A year after Derek started his job, he proposed to Meredith. They started their wedding planning with the idea of a large wedding with everyone they knew, but a week later they ended up deciding that was a stupid idea and a lot of work, so they got married at city hall with Cristina as the maid of honor and Mark as the best man. As soon as they officially got together, Derek started on plans to build a house on the land he had bought. Meredith, even though she was skeptical of the idea of living in a trailer, wound up falling in love with his land.
They now have two children, a son named Cris, after Cristina, and a daughter name Mary, after Mark, plus another one on the way. Meredith turned out to be right about her predictions of becoming a better surgeon than Derek, much to his dismay. She is in her fourth year of being a neuro attending and has already won two Harper Avery's, and now is working on research that will most likely win her a third. Which she claims has nothing to do with the fact that her mother only won two, and she definitely doesn't want to show her dead mother up. Because that would be wrong.
Even though they have been together for over a decade at this point, when ever they are together, sparks fly.