How do William Wordsworth's poems "Daffodils" and "Solitary Reaper" establish him as a poet of nature?

Wordsworth is the poet of nature because, for him, nature isn't just a thing of beauty. Rather, in his works, nature achieves sublimity. He takes it to spiritual and divine heights, acknowledging nature's ability to affect him in these ways.
In "Daffodils," the speaker certainly does appreciate nature's beauty, saying that he "gazed—and gazed—but little thought / What wealth the show to me had brought," speaking of the dancing and "jocund" daffodils that so arrested his attention. It is only later that he realizes the power the memory of those flowers has to impart "bliss" and fill his heart with "pleasure." They have affected his soul, and even just the memory is powerful enough to alter his state of mind and sense of well-being.
In "The Solitary Reaper," the beautiful song of the young woman in nature is enough to fill the vale in which she labors. The speaker says that her voice is even more beautiful than the nightingale or the cuckoo, and her song seems to enhance the natural world around her, emphasizing her connection to nature. Working alone in this natural and innocent setting, girl and song and nature seem to be one, and the music she creates stays with him long after he leaves. He carries it "in [his] heart" now, just like he carries the memory of the daffodils. He has been irrevocably affected for the better.

In both poems ("Daffodils" is often called "I Wandered Lonely as a Cloud"), Wordsworth shows how nature can touch the human soul. He loves nature and explains how long its positive benefits can last. In "I Wandered Lonely as a Cloud," the poet comes across a field of daffodils dancing in the wind before a lake. This simple scene from nature fills him with joy. The sight of the daffodils is "wealth" to him as he gazes at them, transfixed.
"The Solitary Reaper" is slightly different, in that Wordsworth likens a human to a wild creature of nature. Walking in the Scottish Highlands, he is arrested by the beautiful, mournful song a woman sings as she reaps. He compares her song to a nightingale's and a cuckoo's. He says it is even more beautiful. 
In both cases, the poet ends by noting that the natural beauty he saw or heard enters his soul and stays with him. In "The Solitary Reaper," he writes:

The music in my heart I bore, 
Long after it was heard no more.

 
In "I Wandered Lonely as a Cloud," he comments: 
 


For oft, when on my couch I lie 
In vacant or in pensive mood, 
They flash upon that inward eye 
Which is the bliss of solitude; 
And then my heart with pleasure fills, 
And dances with the daffodils.