You can do this:

var base64Icon = 'data:image/png;base64,iVBORw0KGgoAAAANS...';
<Image style={{width: 50, height: 50}} source={{uri: base64Icon}}/>

In the base64Icon variable you need to put your base64 data after data:image/png;base64,. Like this:

var base64Icon = 'data:image/png;base64,{PLACE_YOUR_BASE64_DATA_HERE}';

I use rn-fetch-blob, basically it provides lot of file system and network functions make transferring data pretty easy.

react-native-fetch-blob is deprecated

import RNFetchBlob from "rn-fetch-blob";
const fs = RNFetchBlob.fs;
let imagePath = null;
RNFetchBlob.config({
  fileCache: true
})
  .fetch("GET", "http://www.example.com/image.png")
  // the image is now dowloaded to device's storage
  .then(resp => {
    // the image path you can use it directly with Image component
    imagePath = resp.path();
    return resp.readFile("base64");
  })
  .then(base64Data => {
    // here's base64 encoded image
    console.log(base64Data);
    // remove the file from storage
    return fs.unlink(imagePath);
  });

source Project Wiki

Turns out it's not tricky at all, suppose I have a BASE64 image, if I want to convert it to a JPG, just use react-native-fs like so:

import RNFS from 'react-native-fs';

const imageDate = '<some base64 data>';
const imagePath = `${RNFS.TemporaryDirectoryPath}image.jpg`;

RNFS.writeFile(imagePath, imageData, 'base64')
    .then(() => console.log('Image converted to jpg and saved at ' + imagePath));

That's all

I think Ramsay is wrong, react native have a fully support on base64 image. I found this

https://facebook.github.io/react-native/docs/tabbarios.html

this is a official example of how to create a iOS TabBarController, and they use a base64 image as one of the TabBar's icon.

I think you did not specify the width and the height in the style property of the <Image/>.

I tried to use your base64 image in my React Native Playground, and it works.

Usage

var base64Icon = 'data:image/png;base64,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';

and use in this way

<Image style={{width: 100, height: 50, resizeMode: Image.resizeMode.contain, borderWidth: 1, borderColor: 'red'}} source={{uri: base64Icon}}/>