Use this for adding the background color to the button in iOS:
Styles:
loginScreenButton:{
marginRight:40,
marginLeft:40,
marginTop:10,
paddingTop:10,
paddingBottom:10,
backgroundColor:'#1E6738',
borderRadius:10,
borderWidth: 1,
borderColor: '#fff'
},
loginText:{
color:'#fff',
textAlign:'center',
paddingLeft : 10,
paddingRight : 10
}
Button:
<TouchableOpacity
style={styles.loginScreenButton}
onPress={() => navigate('HomeScreen')}
underlayColor="#fff">
<Text style={styles.loginText}>Login</Text>
</TouchableOpacity>

For Android it simply works with Button color property only:
<Button onPress={onPressAction} title="Login" color="#1E6738" accessibilityLabel="Learn more about this button" />